hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Minimal ideal
In the branch of abstract algebra known as ring theory, a minimal right ideal of a ring R is a non-zero right ideal which contains no other non-zero right ideal. Likewise, a minimal left ideal is a non-zero left ideal of R containing no other non-zero left ideals of R, and a minimal ideal of R is a non-zero ideal containing no other non-zero two-sided ideal of R (Isaacs 2009, p. 190).

In other words, minimal right ideals are minimal elements of the partially ordered set (poset) of non-zero right ideals of R ordered by inclusion.  The reader is cautioned that outside of this context, some posets of ideals may admit the zero ideal, and so the zero ideal could potentially be a minimal element in that poset. This is the case for the poset of prime ideals of a ring, which may include the zero ideal as a minimal prime ideal.

Subset
In mathematics, a set A is a subset of a set B if and only if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.

When quantified,  is represented as

One can prove the statement  by applying a proof technique known as the element argument:

Let sets A and B be given. To prove that 
suppose that a is a particular but arbitrarily chosen element of A
show that a is an element of B.

The validity of this technique can be seen as a consequence of universal generalization: the technique shows  for an arbitrarily chosen element c. Universal generalisation then implies  which is equivalent to  as stated above.
Chesterton Rural District
52°13′05″N 0°08′56″E﻿ / ﻿52.218°N 0.149°E﻿ / 52.218; 0.149

Chesterton was a rural district in Cambridgeshire, England from 1894 to 1974.

It was formed in 1894 as a successor to the Chesterton rural sanitary district.  In 1934, under a County Review Order, its boundaries were altered, taking in the disbanded Swavesey Rural District and part of the disbanded Caxton and Arrington Rural District.  It also ceded an area to the borough of Cambridge.

In 1965 it became part of the new administrative county of Cambridgeshire and the Isle of Ely.

The district was abolished in 1974 under the Local Government Act 1972, and merged with the South Cambridgeshire Rural District to form a new South Cambridgeshire district.

Local Government Act 1929
The Local Government Act 1929 (19 & 20 Geo. 5. c. 17) was an act of the Parliament of the United Kingdom that made changes to the Poor Law and local government in England and Wales.

The act abolished the system of poor law unions in England and Wales and their boards of guardians, transferring their powers to local authorities. It also gave county councils increased powers over highways, and made provisions for the restructuring of urban and rural districts as more efficient local government areas.
Pedro Morales (footballer)
Pedro Andrés Morales Flores (born 25 May 1985) is a Chilean former footballer who played as a midfielder.

He began his professional career with Huachipato before moving to Universidad de Chile, and in 2007 was signed by Dinamo Zagreb of Croatia. After a loan back at Universidad de Chile and Spanish club Málaga, he spent a season with the latter before moving to Vancouver Whitecaps FC, where he served as a captain from 2014 until his departure.

Morales first represented Chile in the 2005 FIFA World Youth Championship, making his senior international debut later in 2008.

MLS Newcomer of the Year Award
The MLS Newcomer of the Year Award is awarded by Major League Soccer to a player who has professional experience in another league and has an outstanding season in his first season of play in MLS. The award was introduced in 2007; its votes are collected from team staff, players, and members of the media.
Sandra Ortega Mera
Sandra Ortega Mera (born 19 July 1968) is a Spanish billionaire heiress, businesswoman and socialite.

Mera is the daughter of Amancio Ortega Gaona, and his first wife Rosalia Mera, the founders of Inditex, best known as the parent company of global fashion empire Zara. She is the second-richest person in Spain, after her father. As of September 2024, Forbes estimated her net worth at US$12.0 billion.

Billionaire
A billionaire is a person whose net worth is at least one billion units of a given currency, typically USD. It is a sub-category of the concept of the ultra high-net-worth individual. The American business magazine Forbes produces a global list of known U.S. dollar billionaires every year and updates an internet version of this list in real time. The American oil magnate John D. Rockefeller became the world's first confirmed billionaire in 1916.

Nineteen individuals had attained the status of centibillionaires, each with a net worth of at least $100 billion, as of January 2026. As of March 2025, there are 3028 billionaires worldwide, with a combined wealth of over $16.1 trillion, up nearly $2 trillion over 2024.
Brahm Singh Tanwar
Brahm Singh Tanwar (born: 7 July 1952) is an Indian politician. He is a former member of the Delhi Legislative Assembly, who joined Aam Aadmi Party in October 2024, after renouncing the membership of Bharatiya Janta Party.

Delhi Legislative Assembly
The Legislative Assembly of the National Capital Territory of Delhi is the unicameral legislature of the union territory of Delhi in India. Delhi Legislative Assembly is the legislative arm of the Government of Delhi. At present, it consists of 70 members, directly elected from 70 constituencies. The tenure of the Legislative Assembly is five years unless dissolved sooner.

The seat of assembly is the Old Secretariat building, which is also the seat of the Government of Delhi.
Gerald Blake (director)
Gerald Blake (3 December 1928 – 5 April 1991) was a British television director who worked in drama from the 1960s to the 1980s.

His numerous credits include The Gentle Touch, The Omega Factor (the episode "After-Image"),  Blake's 7 (the episodes "The Harvest of Kairos" (1980) and "Death-Watch" (1980) from the third series), Survivors (three episodes from the first series), The Onedin Line, Out of the Unknown, Doctor Who (the stories The Abominable Snowmen (1967) and The Invasion of Time (1978)), Dr. Finlay's Casebook, Compact, Z-Cars, Mr. Palfrey of Westminster, and Coronation Street.

The Gentle Touch
The Gentle Touch is a British police procedural drama series made by London Weekend Television for ITV which began on 11 April 1980 and ran until 24 November 1984. The series is notable for being the first British series to feature a female police officer as its leading character, premiering four months ahead of the similarly themed BBC series Juliet Bravo.
St Asaph Rural District
St Asaph Rural District (known as St Asaph (Flint) Rural District until 1934) was a rural district in the administrative county of Flintshire, Wales, from 1894 to 1974.

The district was created by the Local Government Act 1894 from the parts of St Asaph Rural Sanitary District (RSD) in Flintshire. The remainder of the RSD formed St Asaph (Denbigh) Rural District, which was abolished in 1934.

The district comprised nine civil parishes:

Bodelwyddan

Bodfari

Cwm

Dyserth

Meliden

Rhuddlan

St Asaph

Tremeirchion

Waen

The rural district was abolished in 1974 and its area added to the new Borough of Rhuddlan.

Dyserth
Dyserth (Welsh: Diserth) is a village, community and electoral ward in Denbighshire, Wales. Its population at the 2011 United Kingdom census was 2,269 and was estimated by the Office for National Statistics as 2,271 in 2019. It lies within the historic county boundaries of Flintshire. Features include quarrying remains, waterfalls and the mountain Moel Hiraddug. Its railway line, once part of the London and North Western Railway, finally closed in 1973 and is now a footpath.

The village lies on the A5151 road, which links Rhuddlan and Holywell. The nearest major settlements are the coastal towns of Rhyl and Prestatyn.
Rørstad Church
Rørstad Church (Norwegian: Rørstad kirke) is a historic parish church of the Church of Norway in Sørfold Municipality in Nordland county, Norway. It is located in the isolated village of Rørstad. It was once the main church for the Sørfold parish which is part of the Salten prosti (deanery) in the Diocese of Sør-Hålogaland. The white, wooden church was built in a cruciform style in 1761 by an unknown architect. The church seats about 300 people.

Diocese of Sør-Hålogaland
Sør-Hålogaland is a diocese in the Church of Norway. The Diocese covers the Lutheran Church of Norway churches located within Nordland county in Norway. The diocese is headquartered in the town of Bodø at Bodø Cathedral, the seat of bishop Svein Valle (since november 2023).  The diocese is divided into eight deaneries (prosti).
Kling Klang Studio
Kling Klang (also spelled as Klingklang) is the private music studio of the band Kraftwerk. The name is taken from the first song on the Kraftwerk 2 album. The studio was originally located at Mintropstraße 16 in Düsseldorf, Germany, near to Düsseldorf Hauptbahnhof, but in mid-2009 moved to Meerbusch-Osterath, around 10 kilometers west of Düsseldorf. The band also operate a record label named Kling Klang, which they use to release their music.

Minimoog
The Minimoog is an analog synthesizer introduced by Moog Music in 1970. Designed as a more affordable, portable version of the modular Moog synthesizer, it was the first synthesizer sold in retail stores. It was first popular with progressive rock and jazz musicians and found wide use in disco, pop, rock and electronic music. In 2005, the Minimoog was inducted into the TECnology Hall of Fame.

Production of the Minimoog stopped in the early 1980s after the sale of Moog Music. In 2002, the founder, Robert Moog, regained the rights to the Moog brand, bought the company, and released an updated model, the Minimoog Voyager. In 2016 and 2022, Moog Music released newer versions of the original model.
1896 California Golden Bears football team
The 1896 California Golden Bears football team was an American football team that represented the University of California, Berkeley during the 1896 college football season. The team competed as an independent under head coach Frank Butterworth and compiled a record of 6–2–2.

1896 college football season
The 1896 college football season had no clear-cut champion, with the Official NCAA Division I Football Records Book listing Lafayette and Princeton as having been selected national champions.  Lafayette finished with an 11–0–1 record while Princeton had a 10–0–1 record.  In the  second game of the season for both teams, Lafayette and Princeton played to a scoreless tie.  Both teams had signature wins: Lafayette defeated Penn 6–4, giving the Quakers their only loss of the season, while Princeton defeated previously unbeaten Yale, 24–6, on Thanksgiving Day in the last game of the season.  Princeton was retroactively named the 1896 national champions by the Billingsley Report, the Helms Athletic Foundation, the Houlgate System, and Lafayette and Princeton were named national co-champions by the National Championship Foundation and Parke Davis.
Saeid Agin Sagna
Saeid Agin Sagna (born 1975) is a Nigerian retired footballer who appeared in Iranian League between 1991 and 1993. He was son of a Nigerian embassy employee in Tehran. He is the first foreign footballer who played for Bank Tejarat and Poora, and Sanati Kaveh.

Football in Iran
Football is the most popular sport in Iran, with wrestling and volleyball as close contenders. Football has been a part of life for Iranians for many decades now and is played in schools, streets, and football clubs nationwide.

For political and social reasons, women's football grew little from the 1980s to 2020, and clubs such as Persepolis and Esteghlal did not even have a women's football team in these years.
Killip
Killip is a surname of Manx origin, meaning "Philip's son". Notable people with the surname include:

Ben Killip (born 1995), English footballer

Bert Killip (1879–1941), British socialist activist

Ellsworth Paine Killip (1890–1968), American botanist

Chris Killip (1946–2020), Manx photographer

Ellsworth Paine Killip
Ellsworth Paine Killip (September 2, 1890 – November 21, 1968) was a U.S. botanist. His name is linked to over 600 species names. Around 150 species are named for him, including Linanthus killipii. Killip specialized in the taxonomy of South American plants.

Killip joined the staff of the United States National Museum (USNM; now known as the Smithsonian Institution) in 1919 as an Aide in the Division of Plants. He was promoted to Assistant Curator in 1927, Associate Curator in 1928, and Curator in 1946. In 1947, Killip was appointed Head Curator of the newly established Department of Botany, USNM, a position he retained until his retirement in 1950.

In 1925, Killipia was a genus of flowering plants from Colombia and Ecuador, belonging to the family Melastomataceae, named after him. It is now been downgraded to a synonym of Miconia.
Ping Shan Tin Shui Wai Public Library
Ping Shan Tin Shui Wai Public Library (Chinese: 屏山天水圍公共圖書館) is a Hong Kong public library. It is located in Ping Shan Tin Shui Wai Leisure and Cultural Building, on 1 Tsui Sing Road, Tin Shui Wai near MTR Tin Shui Wai station and Light Rail Tin Shui Wai stop. It serves the Ping Shan and Tin Shui Wai neighbourhoods, both administratively in the Yuen Long District, the New Territories.

It is managed by the Hong Kong Public Libraries under the Leisure and Cultural Services Department. It has a total floor space of 6,100 square metres (66,000 sq ft), the second largest public library by area in Hong Kong, only behind the Hong Kong Central Library. It is also the first and only library in Hong Kong to date to have outdoor reading areas. There are about 330,000 books within the library's collection.

Tin Shui Wai station
Tin Shui Wai (Chinese: 天水圍; Cantonese Yale: Tīnséuiwài) is an MTR station on the Tuen Ma line, located in Ping Shan near Tin Shui Wai New Town, Yuen Long District. It is the only heavy rail station serving Tin Shui Wai, which has a population of around 300,000.
Johnson's seagrass
Johnson's seagrass is a small, asexual seagrass in the family Hydrocharitaceae (the "tape-grasses"). It has been called Halophila johnsonii, but is now considered to be a clone of the widespread species Halophila ovalis. As of March 2024, Plants of the World Online treats Halophila johnsonii as a synonym of Halophila ovalis subsp. ovalis. Johnson's seagrass occurs only on the southeastern coast of Florida, in lagoons along roughly 200 km of the Florida coastline between Sebastian Inlet and the northern part of Biscayne Bay, where it grows in small patches of a few centimeters to a few meters in diameter at depths ranging from the intertidal zone down to 3 meters. It was the first marine plant listed on the United States endangered species list, though it was removed from the listing in April 2022.

Sebastian Inlet
Sebastian Inlet, located in Sebastian Inlet State Park in Brevard County, Florida and Indian River County, Florida, offers surfing and fishing opportunities. It is off State Road A1A just 12 miles north of Vero Beach. There are annual surf tournaments, professional and amateur. Visitors fish there, particularly for Snook and Redfish.
The Blue Nowhere
The Blue Nowhere is the eleventh studio album by the American progressive metal band Between the Buried and Me. It was released on September 12, 2025 through InsideOut Music, their first release with the label. It is also their first album without member Dustie Waring since their 2005 release Alaska, and their first as a four-piece band. The song "Things We Tell Ourselves In The Dark" serves as the first single for the band released with a musical video on June 12, 2025. The four-year gap is the longest the band has had between studio albums, since the release of Colors II in 2021.

It was elected by Loudwire as one of the 11 best progressive metal albums of 2025.

Dustie Waring
Robert Dustie Waring (born January 31, 1985) is an American guitarist. He is known as the former guitarist for the progressive metal band Between the Buried and Me. He is also a guitarist for the deathcore band Glass Casket. Waring joined Between the Buried and Me along with Glass Casket bandmate Blake Richardson, replacing Shane Blay as rhythm guitarist.
Abeokuta South
Abeokuta SouthListenⓘ  is a Local Government Area in Ogun State, Nigeria. The headquarters of the LGA are at Ake Abeokuta7°09′00″N 3°21′00″E﻿ / ﻿7.15000°N 3.35000°E﻿ / 7.15000; 3.35000.

It has an area of 71 km2 and a population of 250,278 at the 2006 census.

The postal code of the area is 110.

It was represented by Dimeji Bankole, the former speaker of the House of Representatives, from 2003 to 2011.

Postal code
A postal code (also known locally in various English-speaking countries throughout the world as a postcode, post code, PIN or ZIP Code) is a series of letters or digits or both, sometimes including spaces or punctuation, included in a postal address for the purpose of sorting mail.

As of August 2021, the Universal Postal Union lists 160 countries which require the use of a postal code.

Although postal codes are usually assigned to geographical areas, special codes are sometimes assigned to individual addresses or to institutions that receive large volumes of mail, such as government agencies and large commercial companies. One example is the French CEDEX system.
Kostajnica
Kostajnica can refer to:

Kostajnica, Bosnia and Herzegovina (formerly Bosanska Kostajnica), a town on the right bank of river Una, in Bosnia

Hrvatska Kostajnica, a town on the left bank of river Una, in Croatia

Kostajnica, Doboj, a village near Doboj, Bosnia and Herzegovina

Kostajnica, Konjic, a village near Konjic, Bosnia and Herzegovina

Kostajnica, Bosnia and Herzegovina
Kostajnica (Serbian Cyrillic: Костајница), formerly Bosanska Kostajnica (Serbian Cyrillic: Босанска Костајница), German: Castanowitz, is a town and municipality located in Republika Srpska, Bosnia and Herzegovina. It is situated in the Кrajina region.  As of 2013, the municipality had a population of 5,977 inhabitants, while the town of Kostajnica has a population of 4,047 inhabitants.

The municipality was created from a part of the pre-war municipality of Novi Grad. It is located across the Una river from Hrvatska Kostajnica, Croatia.
Brad L. Mortensen
Brad Leon Mortensen (born October 1, 1970) is an American educator and university administrator who currently serves as the 18th president of Utah State University. He previously served as president of Weber State University from 2018 to 2025. A first-generation college graduate, Mortensen earned degrees from Brigham Young University–Idaho, Utah State University, Syracuse University, and the University of Utah.

Utah System of Higher Education
The Utah System of Higher Education (USHE) is the public university system of the state of Utah. It includes each of the state's sixteen public institutions of higher education, including its eight technical colleges.
Shanmugam Manjunath
Shanmugam Manjunath (23 February 1978 – 19 November 2005) was a sales officer (grade A officer) for the Indian Oil Corporation who was murdered for sealing a corrupt petrol station in Lakhimpur Kheri, Uttar Pradesh. This incident inspired several students at IIM, IIT and other institutes culminating with the IIM students setting up "The Manjunath Shanmugam Trust".

Rabbi Shergill
Rabbi Shergill (born Gurpreet Singh Shergill on 16 April 1973) is an Indian musician well known for his debut album Rabbi and the chart-topper song of 2004, Bullah Ki Jaana  ("I don’t know who I am!"). His music has been described variously as rock, Punjabi, with a bani style melody, and Sufi-style (sufiana), and "semi-Sufi semi-folksy kind of music with a lot of Western arrangements." Shergill has been called "Punjabi music's true urban balladeer".
Pynyonade
Pynyonade or pinionade was a type of confit or confection made with pine nuts and powder-douce in medieval England. Some historic recipes included honey, which may have made it similar to the modern nut brittle. It was imported to England from the Mediterranean in boxes along with other sweets like festucade, citrinade, pomade and gingerbread. There are surviving records showing Katherine de Norwich receiving boxes of pinionade in 1336. The etymology of the word is thought to derive either from the Catalan pinyonada or the Old Occitan pinhonat.

The Forme of Cury gives the recipe as:

Take Almandes iblanced and drawer hem sumdell thicke with gode broth...set on the fire and seeþ it...take Pynes yfryed in oyle oþer in greece and þerto white Powdour douce

Pine nut
Pine nuts, also called piñón (Spanish: [piˈɲon]), pinoli (Italian: [piˈnɔːli]), or pignoli, are the edible seeds of pines (family Pinaceae, genus Pinus). According to the Food and Agriculture Organization, only 29 species provide edible nuts, while 20 are traded locally or internationally owing to their seed size being large enough to be worth harvesting; in other pines, the seeds are also edible but are too small to be of notable value as human food. The biggest exporters of pine nuts are China, Russia, North Korea, Pakistan and Afghanistan.

As pines are gymnosperms, not angiosperms (flowering plants), pine nuts are not "true nuts"; they are not botanical fruits, the seed not being enclosed in an ovary which develops into the fruit, but simply bare seeds—"gymnosperm" meaning literally "naked seed" (from Ancient Greek: γυμνός, romanized: gymnos, lit. 'naked' and σπέρμα, sperma, 'seed'). The similarity of pine nuts to some angiosperm fruits is an example of convergent evolution.
Fennell Hill
Fennell Hill, also known as Cox Site and Milberry Site, is a historic archaeological site located near Peeples, Allendale County, South Carolina. It is a formative shell midden on the Savannah River measuring about 96 meters long by about 48 meters in width.  The midden contains large quantities of fiber-tempered and Thom's Creek pottery—both examples of the earliest pottery found in the southeast.

It was added to the National Register of Historic Places in 1974.

Temper (pottery)
A temper is a non-plastic material added to clay to prevent shrinkage and cracking during drying and firing of vessels made from the clay. Tempers may include:

Some clays used to make pottery do not require the addition of tempers. Pure kaolin clay does not require tempering. Some clays are self-tempered, that is, naturally contain enough mica, sand, or sponge spicules that they do not require additional tempering.
Battle of the Year
Battle of the Year, commonly referred to as BOTY, is an annual international breakdancing competition that began in 1990. It has been regarded as the premier b-boying competition in the world
 and has been referred to as the "World Cup of B-Boying". Regional qualifying tournaments, also known as preliminaries, are held worldwide culminating in the BOTY International, the world finals event which is currently held at Sud de France Arena in Montpellier, France.

For the first twenty-three editions, Battle of the Year was a crew competition; in 2013, a one-on-one competition was added. Since 2014, the one-on-one portion of Battle of the Year is one of ten tournaments that are a part of the World BBoy Series.

The competition spawned the 2007 documentary Planet B-Boy as well as a 2013 eponymously named feature film Battle of the Year, both directed by Benson Lee. It has also gained attention for positive promotion of hip-hop culture and social unity.

Sud de France Arena
Sud de France Arena ("South of France Arena", also known as the Arena Montpellier) is an indoor arena located in the Montpellier suburb of Pérols, Hérault, in the south of France, that opened in September 2010. It has a concert seating capacity of 14,000 spectators, with about 10,000 for sporting events.