hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Perfect ideal
In commutative algebra, a perfect ideal is a proper ideal  in a Noetherian ring  such that its grade equals the projective dimension of the associated quotient ring.

A perfect ideal is unmixed.

For a regular local ring  a prime ideal  is perfect if and only if  is Cohen-Macaulay.

The notion of perfect ideal was introduced in 1913 by Francis Sowerby Macaulay in connection to what nowadays is called a Cohen-Macaulay ring, but for which Macaulay did not have a name for yet. As Eisenbud and Gray point out, Macaulay's original definition of perfect ideal  coincides with the modern definition when  is a homogeneous ideal in a polynomial ring, but may differ otherwise. Macaulay used Hilbert functions to define his version of perfect ideals.

Grade (ring theory)
In commutative and homological algebra, the grade of a finitely generated module  over a Noetherian ring  is a cohomological invariant defined by vanishing of Ext-modules

For an ideal  the grade is defined via the quotient ring viewed as a module over

The grade is used to define perfect ideals. In general we have the inequality

where the projective dimension is another cohomological invariant.

The grade is tightly related to the depth, since

Under the same conditions on  and  as above, one also defines the -grade of  as

This notion is tied to the existence of maximal -sequences contained in  of length .
Río Negro Department
Río Negro Department (Spanish: Departamento de Río Negro, Spanish pronunciation: [ˈri.o ˈneɣɾo]) is a department of the northwestern region of Uruguay. It has an area of 9,282 km2 (3,584 sq mi) and a population of 57,334. Its capital is Fray Bentos. It borders Paysandú Department to the north, Tacuarembó Department to the east, Durazno Department to the southeast, Soriano Department to the south and has the Río Uruguay flowing at its west, separating it from Argentina.

Tacuarembó Department
Tacuarembó (Spanish pronunciation: [takwaɾemˈbo]) is the largest department of Uruguay and it is part of its northern region. Its capital is Tacuarembó. It borders Rivera Department to its north and east, the departments of Salto, Paysandú and Río Negro to its west and has the river Río Negro flowing along its south border, separating it from the departments of Durazno and Cerro Largo.
Hirbnafsah Subdistrict
Hirbnafsah Subdistrict (Arabic: ناحية حربنفسه)  is a Syrian nahiyah (subdistrict) located in Hama District in Hama.  According to the Syria Central Bureau of Statistics (CBS), Hirbnafsah Subdistrict had a population of 54,592 in the 2004 census.

Hama District
Hama District (Arabic: منطقة حماة Ḥamā) is a district (mantiqah) administratively belonging to Hama Governorate, Syria. At the time of the 2023 Census, it had a population of 1,054,000 Its administrative centre is the city of Hama. It is now controlled by the Syrian transitional government
Mendes
Mendes (Ancient Greek: Μένδης, gen.: Μένδητος), the Greek name of the ancient Egyptian city of Djedet, also known in ancient Egypt as Per-Banebdjedet ("The Domain of the Ram Lord of Djedet") and Anpet, is known today as Tell El-Ruba (Arabic: تل الربع).

The city is located in the eastern Nile delta (30°57′30″N 31°30′57″E﻿ / ﻿30.95833°N 31.51583°E﻿ / 30.95833; 31.51583) and was the capital of the 16th Lower Egyptian nome of Kha, until it was replaced by Thmuis in Greco-Roman Egypt. The two cities are only several hundred meters apart. During the 29th Dynasty, Mendes was also the capital of Ancient Egypt, lying on the Mendesian branch of the Nile (now silted up), about 35 km east of al-Mansurah.

Nile Delta
The Nile Delta (Arabic: دلتا النيل, Delta an-Nīl or simply الدلتا, ad-Delta) is the delta formed in Lower Egypt where the Nile River spreads out and drains into the Mediterranean Sea. It is one of the world's largest deltas. From Alexandria in the west to Port Said in the east; it covers 240 km (150 mi) of the Mediterranean coastline and is a rich agricultural region. From north to south the delta is approximately 160 km (100 mi) in length. The Delta begins from Cairo.
2010 Gaza Freedom Flotilla
The 2010 Gaza Freedom Flotilla was a small fleet of ships by the Free Gaza Movement and the Turkish Foundation for Human Rights and Freedoms and Humanitarian Relief (İHH). The Flotilla mission to Gaza had the explicit goal of carrying humanitarian aid and construction materials with the intention of breaking the Israeli blockade of the Gaza Strip. In typical circumstances, aid is first brought to Israel to be inspected and then transferred to Gaza.

On 31 May 2010, Israeli forces boarded the ships in a raid from speedboats and helicopters. Following resistance on one of the boats, nine activists were killed by Israeli forces. Widespread international condemnation of and reaction to the raid followed, Israel–Turkey relations were strained, and Israel subsequently eased its blockade on the Gaza Strip.

Women's Boat to Gaza
The Women's Boat to Gaza (WBG) was an initiative by the Freedom Flotilla Coalition in 2016 to challenge the Israeli naval blockade of the Gaza Strip. The WBG consisted of an entirely female crew and one ship, Zaytouna-Oliva. It started from Barcelona on 14 September 2016 and visited Ajaccio, Corsica and Messina, Sicily along the way. On 5 October 2016, the Israeli Navy intercepted the Women's Boat to Gaza some 14 miles outside the 20-mile "Security Zone" off the Palestinian coast, and detained its crew members, who were taken to the Israeli port of Ashdod. The activists were subsequently deported to their home countries.
Public Health Agency of Sweden
The Public Health Agency of Sweden (Swedish: Folkhälsomyndigheten, FHM) is a Swedish government agency with national responsibility for public health. It falls under the Ministry of Health and Social Affairs and works to promote public health and to prevent illness and injuries through education. It monitors the health of the population, infectious disease control measures, and public health interventions, and assists the Government in its decision-making process by providing facts and knowledge. The agency is tasked with minimizing negative environmental impact on human health, and participates in the work of the EU and international public health organisations, such as the WHO and IANPHI.

Ministry of Health and Social Affairs (Sweden)
The Ministry of Health and Social Affairs (Swedish: Socialdepartementet) is a ministry in the Government of Sweden responsible for policies related to social welfare: social security, social services, medical and health care, public health and the rights of children, the elderly and disabled people.

The ministry is currently headed by the Minister for Social Affairs and Public Health, Jakob Forssmed of the Christian Democrats.
Torii Tadayoshi
Torii Tadayoshi (鳥居 忠吉, died May 7, 1571) was a Japanese samurai of the mid-Sengoku period. Longtime retainer of Matsudaira Hirotada and later, his son Tokugawa Ieyasu. When Ieyasu was sent to Sunpu Castle to be a hostage to the Imagawa clan, Tadayoshi served alongside Matsudaira Shigeyoshi as castle warden of Okazaki Castle. He was renowned as a model of frugality, eventually saving up enough money by the time Ieyasu returned, in order to rearm the Matsudaira (Tokugawa) clan.

Tadayoshi was a father in law of Honda Shigetsugu. 
In later years, he was held up as the model Mikawa-era Tokugawa vassal. After he died, his son, Torii Mototada succeeded the Torii family headship.

Honda Shigetsugu
Honda Shigetsugu (本多 重次) (1529 – August 9, 1596), also known as Honda Sakuzaemon (作左衛門), was a Japanese samurai of the Sengoku period through Azuchi-Momoyama Period, who served the Tokugawa clan. He served as one of Ieyasu's "three magistrates" (san-bugyō).

Shigetsugu was nicknamed "Ogre Sakuza" (鬼作左, Oni Sakuza) for his ferocity.
British Independent Film Award for Best Effects
The British Independent Film Award for Best Effects is an annual award given by the British Independent Film Awards (BIFA) to recognize the best effects in a British independent film. The award was first presented in the 2017 ceremony.

Prior to 2017, visual effects were included in the category Best Technical Achievement alongside different areas of crafts in film, this category was presented from 2001 to 2016.

British Independent Film Awards
The British Independent Film Awards (BIFA) is an organisation that celebrates, supports, and promotes British independent cinema and film-making talent in the United Kingdom. Nominations for the annual awards ceremony are announced in early November, with the ceremony itself taking place in early December.

Since 2015, BIFA has also hosted UK-wide talent development and film screening programmes, with the support of Creative Skillset and the  British Film Institute.
Yarnbrook
Yarnbrook is a large hamlet in Wiltshire, England, between the towns of Westbury and Trowbridge. Most of the settlement lies in the civil parish of North Bradley, the rest in West Ashton. Most of Yarnbrook's houses line the A350 road, running between the M4 motorway near Chippenham and the south coast of England at Poole, Dorset.

West Ashton
West Ashton is a village and civil parish in Wiltshire, England. It is about 2 miles (3.2 km) southeast of Trowbridge, near the A350 between Melksham and Yarnbrook which bypasses Trowbridge. The parish includes the hamlets of Dunge (grid reference ST 892 544), East Town (ST 893 557) and Rood Ashton (ST 886 560).

West Ashton was anciently a tithing – alongside Great Hinton and Semington – of the large Steeple Ashton parish, within the hundred of Whorwellsdown. These tithings became separate civil parishes in the late 19th century.

The village has a primary school, West Ashton Church of England Primary School, and a village hall.
Wallender Born
The Wallender Born or Wallenborn (popularly known as the Brubbel) is a cold water geyser in the village Wallenborn (Eifel district, Germany). It is adjacent to the reactivated Andernach Geyser (aka Namedyer Sprudel) an active cold water geyser in Germany.

Experts disagree on whether the Wallender Born can be described as eruptive course, but periodic gas outbreaks have been witnessed since time immemorial. Until being drilled, Wallender Born was therefore at least a (periodic) mofette. The high water surge of a typical hot spring was found only after construction work. The fountain is operated geyser-like: The artificial conduit is located below the water surface of a small pond. The water is therefore not thrown like a fountain, but turbulent. The "fuel gas" of the geyser is carbon dioxide. It contains traces of other gases like hydrogen sulfide which leads to a smell reminiscent of rotten eggs.

Cold-water geyser
Cold-water geysers are geysers that have eruptions whose water spurts are propelled by CO2 bubbles, instead of the hot steam  which drives the more familiar hot-water geysers: The gush of a cold-water geyser is identical to the spurt from a freshly-opened bottle of soda pop.
Cold-water geysers look quite similar to their steam-driven counterparts; however, their CO2-laden water often appears whiter and more frothy.
Jun Togawa
Jun Togawa (戸川純, Togawa Jun; born 31 March 1961) is a Japanese singer, musician and actress. She is one of the greatest influences on Japanese avant-garde music and media, and her career spans over 35 years. Her close friends over the years include Susumu Hirasawa. She was mainly active from 1981 to 1995.

Alfa Records
Alfa Records Inc. (アルファレコード株式会社, Alfa Record Kabushiki Gaisha), originally a publisher known as Alfa Music Ltd. and later succeeded by record company Alfa Music Inc., was established in 1969 by composer and record producer Kunihiko Murai. It was formed into an independent record label known as Alfa Records in 1977. A short-lived American subsidiary operated from 1980 to 1982.
Abdul Matlib Mazumdar
Abdul Matlib Mazumder (1890–1980) was an Indian freedom fighter and political leader based in undivided Assam State. In 1946, when India was still under British rule, he became an MLA and Cabinet Minister of Assam.  He was one of the prominent Muslim leaders of eastern India to support Hindu-Muslim unity, opposing the partition of India on communal lines. Mazumder along with Fakhruddin Ali Ahmed (who later became the 5th President of India) became the most prominent Muslim opponents of the demand for a separate Muslim state of Pakistan, especially in the eastern part of the country.

Barak Valley
Barak Valley is the southernmost region and administrative division of the Indian state of Assam. It is named after the Barak River, whose watershed roughly forms its northern border. The Barak valley consists of three administrative districts of Assam: Cachar, Karimganj, and Hailakandi. The main and largest city is Silchar, which seats the headquarter of Cachar district and also serves as administrative divisional office of Barak valley division. The valley is bordered by Mizoram and Tripura to the south, Bangladesh and Meghalaya to the west and Manipur to the east respectively. Once North Cachar Hills was a part of Cachar district which became a subdivision in 1951 and eventually a separate district. On 1 July 1983, Karimganj district was curved out from the eponymous subdivision of Cachar district. In 1989, the subdivision of Hailakandi was upgraded into Hailakandi district.
2015 FIBA COCABA Championship
The 2015 Men's FIBA COCABA Championship was the regional basketball championship of FIBA Americas for the Central American and Caribbean subzones. The top 3 national teams qualified to 2016 Centrobasket. The tournament was held in the city of San José, Costa Rica, from 16 to 20 September 2015.

2016 Centrobasket
The 2016 Men's Central American and Caribbean Basketball Championship, also known as 2016 Centrobasket, was the regional basketball championship of FIBA Americas for the Central American and Caribbean subzone. The top five teams qualified for the 2017 FIBA AmeriCup; the top seven teams qualified for the 2019 FIBA Basketball World Cup qualification and for the 2018 Central American and Caribbean Games. The tournament was held in the Panama City from 19 to 25 June 2016.

Puerto Rico won their 11th Centrobasket title by defeating Mexico in the final, 84–83.
Miyanokoshi-juku
Miyanokoshi-juku (宮ノ越宿, Miyanokoshi-juku) was the thirty-sixth of the sixty-nine stations of the Nakasendō, as well as the fourth of eleven stations on the Kisoji. It is located in the present-day town of Kiso, in the Kiso District of Nagano Prefecture, Japan.

69 Stations of the Nakasendō
The 69 Stations of the Nakasendō (中山道六十九次, Nakasendō Rokujūkyū-tsugi) are the rest areas along the Nakasendō, which ran from Nihonbashi in Edo (modern-day Tokyo) to Sanjō Ōhashi in Kyoto. The route stretched approximately 534 km (332 mi) and was an alternate trade route to the Tōkaidō.
Hashmal
The Hashmallim (Hebrew: חַשְׁמַלִּים Ḥašmallīm; sing. Hashmal, חַשְׁמַל Ḥašmal; rendered amber by the Authorized Version) are angelic entities in Judaism.

The word hashmal appears in the Hebrew Bible in Ezekiel 1:4-5:

And I looked, and, behold, a stormy wind came out of the north, a great cloud, with a fire flashing up, so that a brightness was round about it; and out of the midst thereof as the colour of electrum, out of the midst of the fire. And out of the midst thereof came the likeness of four living creatures. And this was their appearance: they had the likeness of a man.

Hashmallim occupy the fourth rank of ten in Maimonides' exposition of the Jewish angelic hierarchy.

The Septuagint translates hashmal to ηλεκτρον (elektron), which means "amber" in English. Later, hashmal became the Modern Hebrew word that translates to the English word "electricity". Jewish poet Judah Leib Gordon coined the modern Hebrew word, in his 1878 collection Gabashta.

Angels in Judaism
In Judaism, angels (Hebrew: מַלְאָךְ, romanized: mal’āḵ, lit. 'messenger', plural: מַלְאָכִים mal’āḵīm) are supernatural beings that appear throughout the Tanakh (Hebrew Bible), Rabbinic literature, Jewish apocrypha, Christian pseudepigrapha, Jewish philosophy, Jewish mysticism, and traditional Jewish liturgy as agents of the God of Israel. They are categorized in different hierarchies. Their essence is often associated with fire. The Talmud describes their very essence as fire.
James Ellroy
Lee Earle "James" Ellroy (born March 4, 1948) is an American crime fiction writer and essayist. Ellroy has become known for a telegrammatic prose style in his most recent work, wherein he frequently omits connecting words and uses only short, staccato sentences, and in particular for the novels The Black Dahlia (1987) and L.A. Confidential (1990).

This Storm (novel)
This Storm: A Novel is a 2019 historical fiction and crime fiction by American author James Ellroy. It is the second novel in Ellroy's "Second L.A. Quartet", in reference to the first "L.A. Quartet", and following the novel Perfidia. Ellroy dedicated the novel "To HELEN KNODE." The epigraph is "Blood alone moves the wheels of history. -Benito "Il Duce" Mussolini". It was released May 30, 2019, in the United Kingdom, and June 4, 2019 in the United States.
Lexington Centre
42°26′53.8″N 71°13′41.4″W﻿ / ﻿42.448278°N 71.228167°W﻿ / 42.448278; -71.228167

Lexington Centre (often spelled Center since the 1980s), often simply called the Centre by locals, is both the geographic and retail center of Lexington, Massachusetts on Massachusetts Avenue.  It is home to numerous restaurants, banks, retail shops, beauty parlors, a small cinema, a museum, the Cary Memorial Library, and many historic landmarks, including Lexington Common.

Lexington, Massachusetts
Lexington is a suburban town in Middlesex County, Massachusetts, United States, located 10 miles (16 km) from Downtown Boston. The population was 34,454 as of the 2020 census.  The area was originally inhabited by Native Americans, and was first settled by Europeans c. 1642 as a farming community. Lexington is well known as the site of the first shots of the American Revolutionary War, in the Battle of Lexington on April 19, 1775, where the "Shot heard 'round the world" took place. It is home to Minute Man National Historical Park.
Healthier Lives
Healthier Lives – He Oranga Hauora was one of New Zealand's eleven collaborative research programmes known as National Science Challenges. Running from 2015 to 2024, the focus of Healthier Lives National Science Challenge research was cancer, cardiovascular disease, obesity, and diabetes in the New Zealand population, encompassing prevention, treatment, and the reduction of health inequity, and including precision medicine techniques, and culturally-centred health programmes for Māori and Pasifika.

Jim Mann (scientist)
Sir Joel Ivor Mann KNZM (born 30 September 1944), generally known as Jim Mann, is a New Zealand nutritionist and endocrinologist. He is professor in human nutrition and medicine at the University of Otago and consultant physician (endocrinology) at Dunedin Hospital. He has researched the role of lipids and carbohydrates in coronary heart disease, diabetes, and obesity, as well as the relationship between obesity and cancer. He was knighted in the 2022 New Year Honours.
Valdian Rural District
Valdian Rural District (Persian: دهستان ولديان) is in Ivughli District of Khoy County, West Azerbaijan province, Iran. Its capital is the village of Mahlezan. The previous capital of the rural district was the village of Saidabad. It is home to Iran's nuclear facilities.

Saidabad, Khoy
Saidabad (Persian: سعيداباد) is a village in Gowharan Rural District of the Central District in Khoy County, West Azerbaijan province, Iran. It was the capital of Valdian Rural District in Ivughli District until its capital was transferred to the village of Mahlezan.
Santa Rosa River (Acre)
Santa Rosa River is a river of Acre state in western Brazil, a tributary of the Purus River.

The river defines the boundary between Peru and Brazil in the centre of the state of Acre, then runs for a short distance along the boundary of the 231,555 hectares (572,180 acres) Santa Rosa do Purus National Forest, a sustainable use conservation unit created in 2001, until it joins the Purus River opposite the community of Santa Rosa do Purus.

Purus River
The Purus River (Portuguese: Rio Purus; Spanish: Río Purús) is a tributary of the Amazon River in South America. Its drainage basin is 371,042 km2 (143,260 sq mi), and the mean annual discharge is 11,207 m3/s (395,800 cu ft/s). The river shares its name with the Alto Purús National Park and the Purús Province (and its conformed Purús District), one of the four provinces of Peru in the Ucayali Region.
Windermere, Cumbria (town)
Windermere (/ˈwɪndərmɪər/) is a town in the civil parish of Windermere and Bowness, in the Westmorland and Furness district in the ceremonial county of Cumbria, England; it is within the Lake District National Park. The town lies about half a mile (1 km) east of the lake, Windermere, from which it takes its name. In 2021 it had a population of 4,826.

While Windermere town does not itself touch the lake, it forms one urban area with the older town of Bowness-on-Windermere, which is directly on the lake shore. Windermere began to grow when the railway station and hotel of the same name opened in 1847. Tourism is popular in the town, owing to its proximity to the lake and local scenery. Boats from the piers in Bowness sail around the lake, many calling at Ambleside or at Lakeside where there is a restored railway.

Windermere Hotel (Lake District)
Windermere Hotel , originally The Riggs Windermere, is a hotel in Windermere, Cumbria, England, located near Windermere railway station. The hotel opened at the time that the railway link with Kendal was established in 1847. It overlooks the A591 road.
Hamilton State School
Hamilton State School is a heritage-listed state school at Oxford Street, Hamilton, City of Brisbane, Queensland, Australia. It was built in 1907. It was added to the Queensland Heritage Register on 30 November 2018.

Hamilton, Queensland
Hamilton is a riverside mixed-use suburb in the north-east of the City of Brisbane, Queensland, Australia. Hamilton is located along the north bank of the Brisbane River. In the 2021 census, Hamilton had a population of 8,922 people.
Binalong railway station
Binalong railway station is a closed railway station on the Main Southern railway line, serving the village of Binalong, New South Wales, Australia. The original station opened in Binalong in November 1876 on the original rail alignment, which was bypassed with a deviation in 1916. The new island station opened on the new alignment in 1916 and is now closed to passenger services. It survives in good condition. The original station on the old alignment is in use as a private residence.

Main Southern railway line
The Main Southern railway line (or Great Southern Railway) is a major railway in New South Wales, Australia. It runs from Sydney to Albury, near the Victorian border. The line passes through the Southern Highlands, Southern Tablelands, South West Slopes and Riverina regions.
Demoutsantata
Demoutsantata (Greek: Δεμουτσαντάτα, before 1940: Μοντεσαντάτα - Montesantata) is a village in the municipal unit of Argostoli on the island of Kefalonia, Greece. It is part of the community of Troianata. It is located 1 km south of Troianata and 6 km southeast of Argostoli.

Troianata
Troianata (Greek: Τρωιανάτα) is a village and a community in the municipal unit of Argostoli, on the island of Cephalonia, Greece. The community consists of the villages Troianata, Demoutsantata and Mitakata. Troianata is situated on a hillside, at about 300 m elevation. It is 3 km north of Peratata, 3 km southwest of Valsamata and 6 km southeast of Argostoli. Troianata suffered great damage from the 1953 Ionian earthquake.