hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Eakin–Nagata theorem
In abstract algebra, the Eakin–Nagata theorem states: given commutative rings  such that  is finitely generated as a module over , if  is a Noetherian ring, then  is a Noetherian ring. (Note the converse is also true and is easier.)

The theorem is similar to the Artin–Tate lemma, which says that the same statement holds with "Noetherian" replaced by "finitely generated algebra" (assuming the base ring is a Noetherian ring).

The theorem was first proved in Paul M. Eakin's thesis (Eakin 1968) and later independently by Masayoshi Nagata (1968). The theorem can also be deduced from the characterization of a Noetherian ring in terms of injective modules, as done for example by David Eisenbud in (Eisenbud 1970); this approach is useful for a generalization to non-commutative rings.

Noncommutative ring
In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring.

Noncommutative algebra is the part of ring theory devoted to study of properties of the noncommutative rings, including the properties that apply also to commutative rings.

Sometimes the term noncommutative ring is used instead of ring to refer to an unspecified ring which is not necessarily commutative, and hence may be commutative. Generally, this is for emphasizing that the studied properties are not restricted to commutative rings, as, in many contexts, ring is used as a shorthand for commutative ring.

Although some authors do not assume that rings have a multiplicative identity, in this article we make that assumption unless stated otherwise.
North Korean occupation of South Korea
The North Korean occupation of South Korea from June to September 1950 constituted the first phase of the Korean War.

On June 25, 1950, The Korean People's Army (KPA) crossed the 38th parallel between North and South Korea. The KPA advanced at an incredible speed, capturing Seoul on June 28, 1950. Thus began the three-months of North Korean occupation in South Korea. This occupation ceased after the UN launched a counteroffensive in September 30 following the landing on Inchon. This period of occupation is commonly described as "(Korea) under people's republican rule" (Korean: 인공 치하; Hanja: 人共治下; RR: Ingong-chiha).

Korean People's Army
The Korean People's Army (KPA; Korean: 조선인민군; MR: Chosŏn inmin'gun) encompasses the combined military forces of North Korea and the armed wing of the Workers' Party of Korea (WPK). The KPA consists of five branches: the Ground Force, the Naval Force, the Air Force, the Strategic Force, and the Special Operations Forces. It is commanded by the WPK Central Military Commission, which is chaired by the WPK general secretary, and the president of the State Affairs; both posts are currently headed by Kim Jong Un.

The KPA considers its primary adversaries to be the Republic of Korea Armed Forces and United States Forces Korea, across the Korean Demilitarized Zone, as it has since the Armistice Agreement of July 1953. As of 2021 it is the second largest military organisation in the world, with 29.9% of the North Korean population actively serving, in reserve or in a paramilitary capacity.
Herbert Lawford
Herbert Fortescue Lawford (15 May 1851 – 20 April 1925) was a former world No. 1 tennis player from Scotland who won the Men's Singles championship at Wimbledon in 1887, and was runner-up a record five times (shared with Arthur Gore).

World number 1 ranked male tennis players
World number 1 ranked male tennis players is a year-by-year listing of the male tennis players who were ranked as world No. 1 by various contemporary and modern sources. The annual source rankings from which the No. 1 players are drawn are cited for each player's name, with a summary of the most important tennis events of each year also included. If world rankings are not available, recent rankings by tennis writers for historical years are accessed, with the dates of the recent rankings identified. In the period 1948–1953, when contemporary professional world rankings were not created, the U.S. professional rankings are cited.
Ng Yu Zhi
Ng Yu Zhi (born c. 1987), also known as Ng You Zhi, is a Singaporean alleged con artist and fraudster. The former director of Envy Global Trading, he was charged in March 2021 with running the largest Ponzi scheme in the history of Singapore, worth about S$1.5 billion.

Singapore dollar
The Singapore dollar (sign: S$; code: SGD) is the official currency of the Republic of Singapore. It is divided into 100 cents (Malay: sen, Chinese: 分; pinyin: fēn, Tamil: காசு, romanized: kācu). It is normally abbreviated with the dollar sign $, or S$ to distinguish it from other dollar-denominated currencies. The Monetary Authority of Singapore (MAS) issues the banknotes and coins of the Singapore dollar.

As of 2024, the Singapore dollar is the 13th most traded currency in the world. Apart from its use in Singapore, the Singapore dollar is also accepted as customary tender in Brunei according to the Currency Interchangeability Agreement between the Monetary Authority of Singapore and the Autoriti Monetari Brunei Darussalam (Monetary Authority of Brunei Darussalam). Likewise, the Brunei dollar is also customarily accepted in Singapore.
Sergei Nikolaevich Trubetskoy
Prince Sergei Nikolaevich Trubetskoy (Russian: Серге́й Никола́евич Трубецко́й; 4 August [O. S. 23 June] 1862 – 23 September 1905) was a Russian religious philosopher. He was the son of Prince Nikolai Petrovitch Trubetskoy, co-founder of the Moscow Conservatory, and Sophia Alekseievna Lopouchina, who was a big influence on his religious thought. Trubetskoy and his brother, Evgenii Nikolaevitch Troubetzkoy (1863–1920), continued Vladimir Solovyov's work on developing a modern Christian philosophy of the world. He was also a professor of philosophy at Moscow University and a founding member of the underground discussion circle Beseda.

DjVu
DjVu is a computer file format designed primarily to store scanned documents, especially those containing a combination of text, line drawings, indexed color images, and photographs. It uses technologies such as image layer separation of text and background/images, progressive loading, arithmetic coding, and lossy compression for bitonal (monochrome) images. This allows high-quality, readable images to be stored in a minimum of space, so that they can be made available on the web.

DjVu has been promoted as providing smaller files than PDF for most scanned documents. The DjVu developers report that color magazine pages compress to 40–70 kB, black-and-white technical papers compress to 15–40 kB, and ancient manuscripts compress to around 100 kB; a satisfactory JPEG image typically requires 500 kB. Like PDF, DjVu can contain an OCR text layer, making it easy to perform copy and paste and text search operations.
Sighthill, Glasgow
Sighthill is a neighbourhood in the Scottish city of Glasgow. It is situated north of the River Clyde and is part of the wider Springburn district in the north of the city. It is bordered to the north by Cowlairs, to the east by the Springburn Bypass road and the Royston neighbourhood, to the west by the Glasgow to Edinburgh via Falkirk Line (running into Queen Street Station) and to the south by the Townhead interchange of the M8 Motorway.

The district is primarily residential and from the mid-1960s consisted of a housing estate split into two sub-areas –  Pinkston to the south and Fountainwell to the north – each with five 20-storey 'slab' tower blocks, plus seven 5-storey maisonette blocks and five rows of tenements in between. Most of these buildings were demolished during the early 21st century and replaced by new housing with associated infrastructure and landscaping.

M8 motorway (Scotland)
The M8 is the busiest motorway in Scotland. It connects the country's two largest cities, Glasgow and Edinburgh, and serves other large communities including Airdrie, Coatbridge, Greenock, Livingston and Paisley. The motorway is 60 miles (97 km) long. A major construction project to build the final section between Newhouse and Baillieston was completed on 30 April 2017.  The motorway has one service station, Heart of Scotland Services, previously named Harthill due to its proximity to the village.
Parszkowo
Parszkowo [parʂˈkɔvɔ] is a village in the administrative district of Gmina Krokowa, within Puck County, Pomeranian Voivodeship, in northern Poland.

For details of the history of the region, see History of Pomerania.

Puck County
Puck County (Polish: powiat pucki, Kashubian: pùcczi pòwiat) is a unit of territorial administration and local government (powiat) in Pomeranian Voivodeship, northern Poland, on the Baltic coast. The powiat of this name existed  in the history of Poland, since the times of the Polish–Lithuanian Commonwealth up to 1795, and then reintroduced in 1999.
2009 Australian Manufacturers' Championship
The 2009 Australian Manufacturers' Championship was a CAMS sanctioned motor racing title for car manufacturers. It was the 24th manufacturers title to be awarded by CAMS and the 15th to be contested under the Australian Manufacturers' Championship name. The championship was open to Group 3E Series Production Cars. Mitsubishi ended the season as champions, beating other manufacturers Toyota and Subaru.

Motorsport Australia
Motorsport Australia, formerly the Confederation of Australian Motor Sport (CAMS), is the nationally recognised governing and sanctioning body for four-wheeled motorsport in Australia. It is affiliated with the Federation Internationale de l'Automobile (FIA).
Tipu Aziz
Tipu Zahed Aziz (Bengali: টিপু আজিজ জাহেদ; 9 November 1956 – 25 October 2024) was a Bangladeshi-born British professor of neurosurgery at the John Radcliffe Hospital in Oxford, Aarhus Denmark and Porto, Portugal. He specialised in the study and treatment of Parkinson's disease, multiple sclerosis, dystonia, spasmodic torticollis, fixed abnormal posture of the neck, tremor, and intractable neuropathic pain. Besides his medical work, he was also notable as a public commentator in support of animal experimentation.

John Radcliffe Hospital
John Radcliffe Hospital (informally known as the JR or the John Radcliffe) is a large tertiary teaching hospital in Oxford, England. It is a part of the Oxford University Hospitals NHS Foundation Trust and is named after John Radcliffe, an 18th-century physician and Oxford University graduate, who endowed the Radcliffe Infirmary, the main hospital for Oxford from 1770 until 2007.

It is the main teaching hospital for Oxford University and Oxford Brookes University, and incorporates the Oxford University Medical School.
Sri Ramakrishna College, Akkaraipattu
Sri Ramakrishna College, located in Akkaraipattu, Sri Lanka, is a prominent national school known for its educational programs and community involvement. The college serves students from various backgrounds and emphasizes a comprehensive approach to learning in the Ampara District within the Eastern Province of Sri Lanka.

Ampara District
Ampara District (Tamil: அம்பாறை மாவட்டம், romanized: Ampāṟai Māvaṭṭam; Sinhala: අම්පාර දිස්ත්‍රික්කය, romanized: Ampāra Distrikkaya) is one of the 25 districts of Sri Lanka, the second-level administrative divisions of the country. The district is administered by a District Secretariat headed by a District Secretary (previously known as a Government Agent) appointed by the central government of Sri Lanka. The capital of the district is the town of Ampara. The district was carved out of the southern part of Batticaloa District in April 1961.
Tatjana Kozlova-Johannes
Tatjana Kozlova-Johannes (born 8 January 1977 in Narva) is an Estonian-Russian composer.

In 2000s, she graduated from Estonian Academy of Music and Theatre in composition speciality.

As of about 2020, she is teaching the composition at Georg Ots Tallinn Music School.

In 2015, she received Annual Prize of the Endowment for Music of the Cultural Endowment of Estonia.

Since 2004, she is a member of Estonian Composers' Union.

She received in 2022 the Lepo Sumera Composition Prize.

Estonian Academy of Music and Theatre
The Estonian Academy of Music and Theatre (Eesti Muusika- ja Teatriakadeemia) began as a mixed choir of the Estonia Society Musical Department (EMD) on the eve of World War I. The assembly of the Estonia Society created the Tallinn Higher Music School on November 17, 1918. The opening ceremony took place on September 28, 1919. In 1923 the educational institution was renamed the Tallinn Conservatoire.  In 1938 the State Drama School was opened. In 1993 the school was renamed the Estonian Academy of Music. In 1995 the Drama Faculty was renamed the Higher Theatre School.

Some prominent graduates of the Estonian Academy of Music include singers Aile Asszonyi, Heli Lääts, and Ain Anger, conductors Roman Matsov, Tõnu Kaljuste, Olari Elts, Eri Klas, and Kristiina Poska, composers Arvo Pärt, Lepo Sumera, Erkki-Sven Tüür and Ardo Ran Varres, director Andres Puustusmaa, and actors Tõnu Aav, Heino Mandri, Elmo Nüganen, Ain Lutsepp, Margus Oopkaup, Jan Uuspõld, Tõnu Tepandi and Taavi Eelmaa.
Maria Lani
Maria Lani (Maria Jeleniewicz; 24 June 1895 – 1954) was an aspiring film actress and artists' model. In the late 1920s she was portrayed in paintings and sculpture by over 50 artists, including Bonnard, Chagall, Cocteau, Derain, Matisse, Rouault, and Suzanne Valadon.

Pierre Bonnard
Pierre Bonnard (French: [pjɛʁ bɔnaʁ]; 3 October 1867 – 23 January 1947) was a French painter, illustrator and printmaker, known especially for the stylized decorative qualities of his paintings and his bold use of color. A founding member of the Post-Impressionist group of avant-garde painters Les Nabis, his early work was strongly influenced by the work of Paul Gauguin, as well as the prints of Hokusai and other Japanese artists. Bonnard was a leading figure in the transition from Impressionism to Modernism. He painted landscapes, urban scenes, portraits and intimate domestic scenes, where the backgrounds, colors and painting style usually took precedence over the subject.
Angkor Thom district
Angkor Thom (Khmer: ស្រុកអង្គរធំ) is an administrative district of Siem Reap province, in north western Cambodia. According to the 1998 census of Cambodia, it had a population of 17,750.

The archaeological site of Angkor Thom is not located in this district, but in Siem Reap Municipality (Sangkat of Kouk Chak and Nokor Thum).

Angkor Thom
Angkor Thom (Khmer: អង្គរធំ [ʔɑŋkɔː tʰom]; meaning "Great City"), alternatively Nokor Thom (Khmer: នគរធំ [nɔkɔː tʰom]), located in present-day Cambodia, was the last and most enduring capital city of the Khmer Empire. It was established in the late twelfth century by King Jayavarman VII.: 378–382 : 170  It covers an area of 9 km², within which are located several monuments from earlier eras as well as those established by Jayavarman and his successors. At the centre of the city is Jayavarman's state temple, the Bayon, with the other major sites clustered around the Victory Square immediately to the north. The site is one of the major tourist attractions of Southeast Asia.
Mike Freiberg
Mike Freiberg (born September 23, 1976) is an American politician serving in the Minnesota House of Representatives since 2013. A member of the Minnesota Democratic–Farmer–Labor Party (DFL), Freiberg represents District 43B in the central Twin Cities metropolitan area, which includes the cities of Golden Valley and Robbinsdale and parts of Hennepin County.

Minnesota Democratic–Farmer–Labor Party
The Minnesota Democratic–Farmer–Labor Party (DFL) is a political party in the U.S. state of Minnesota affiliated with the national Democratic Party. The party was formed by a merger between the Minnesota Democratic Party and the Minnesota Farmer–Labor Party in 1944. The DFL is one of two state Democratic Party affiliates with a different name from that of the national party, the other being the neighboring North Dakota Democratic–Nonpartisan League Party.

The DFL controls four of Minnesota's eight United States House of Representatives seats, both of its United States Senate seats, the Minnesota Senate, and all other statewide offices, including the Governor of Minnesota, making it the dominant party in the state. In the Minnesota House of Representatives, it has a power-sharing agreement with its main political rival, the Republican Party of Minnesota, following a tie in the 2024 Minnesota House of Representatives election.
Swimming at the 2005 World Aquatics Championships – Men's 100 metre butterfly
The Men's 100 Butterfly at the 2005 FINA World Aquatics Championships was swum 29 – 30 July 2005 in Montreal, Canada. Preliminary and Semifinals heats were held on 29 July, with the top-16 finishers from the Prelims in the mornings advancing to swim again in Semifinals that evening. The top-8 swimmers from the Semifinals then advanced to swim the race a third time in the Final the next evening (30 July).

This race consists of 2 lengths of butterfly, in the long course (50m) pool the event was swum in.

At the start of the event, the existing World (WR) and Championships (CR) records were:

The following records were established during the competition:

Butterfly stroke
Butterfly (shortened to fly) is a swimming stroke swum on the front, with both arms moving symmetrically, accompanied by the butterfly kick (also known as the "dolphin kick") along with the movement of the hips and chest.

It is the newest swimming style swum in competition, first swum in the early 1950s and originating from breaststroke.

For most competitive swimmers, butterfly is the second fastest stroke, only slower than front crawl.
Sinah, Hayling Island
Sinah is the area at the southwestern end of Hayling Island. It incorporates the Ferrypoint, Sinah Beach, The Kench, Sinah Warren, and Sinah Common. It is bounded to the east by West Town. Langstone Harbour and its entrance form the north and west borders, and to the south is Hayling Bay.

Duke of Norfolk
Duke of Norfolk is a title in the Peerage of England. The premier non-royal peer, the Duke of Norfolk is additionally the premier duke and earl in the English peerage. The seat of the Duke of Norfolk is Arundel Castle in Sussex, although the title refers to the county of Norfolk. The current duke is Edward Fitzalan-Howard, 18th Duke of Norfolk. The dukes have historically been Catholic, a state of affairs known as recusancy in England.

All past and present dukes have been descended from Edward I. The son of Thomas Howard, 3rd Duke of Norfolk, was Henry Howard, Earl of Surrey; the earl was descended from Edward III. As all subsequent dukes after Thomas Howard, 4th Duke of Norfolk are descendants of the Earl of Surrey, this means they are also descended from Edward III.
Abbey Lee
Abbey Lee Kershaw (born 12 June 1987) is an Australian model, actress and musician. Following several years of success leading up to the 2011 fashion seasons, V magazine dubbed her a supermodel, and Models.com has listed her as an "Industry Icon". She dropped the use of her surname, Kershaw, in 2015.

Paris Fashion Week
Paris Fashion Week (French: Semaine de la mode de Paris, commonly [la] Fashion Week) is a series of designer presentations held semi-annually in Paris, France, with spring/summer and autumn/winter events held each year. Dates are determined by the Fédération de la Haute Couture et de la Mode. Paris Fashion Week is held at venues throughout the city. It is one of the "Big Four" fashion weeks alongside New York, Milan, and London.

In addition to ready-to-wear shows, there are men's and haute couture shows; these are held semiannually for the spring/summer and autumn/winter seasons. The haute couture collections are always presented and exhibited before the ready-to-wear collections, with there being a total of a little over 100 collections each season. Also, every year, famous brands like Dior, Chanel, Louis Vuitton, Kenzo, Givenchy, and Céline host their shows in historical places such as the Carrousel du Louvre and the Grand Palais.
Chessington Computer Centre
Chessington Computer Centre was an organisation based in Chessington that provided administration services to the UK Government. Originally part of central government, it became an executive agency and trading fund of the Cabinet Office on 1 April 1993. In July 1996 it was sold to a management and employee buy-out team for £12.5 million. It was acquired by Automatic Data Processing in September 1998, but was later closed in June 2005.

The chess player Michael Basman worked  at the Chessington Computer Centre as a computer programmer.

Executive agency
An executive agency is a part of a government department that is treated as managerially and budgetarily separate, to carry out some part of the executive functions of the United Kingdom government, Scottish Government, Welsh Government or Northern Ireland Executive. Executive agencies are "machinery of government" devices distinct both from non-ministerial government departments and non-departmental public bodies (or "quangos"), each of which enjoy legal and constitutional separation from ministerial control.  The model has been applied in several other countries.
Sass Rogando Sasot
Sass Rogando Sasot is Filipino blogger and transgender rights activist who is a supporter of President Rodrigo Duterte and known for spreading disinformation. She is also co-founder of the Society of Trans Women of the Philippines in 2002.

Jay Tarriela
Jay Tristan Tarriela is a Philippine Coast Guard (PCG) officer with the rank of rear admiral currently serving as the organization's spokesperson. He has contributed to maritime security and policy by publicly supporting the Philippines’ position in the territorial disputes in the South China Sea.
Kampong Mulaut
Kampong Mulaut is a village in Brunei-Muara District, Brunei, about 14 kilometres (8.7 mi) from the capital Bandar Seri Begawan. The population was 5,846 in 2016. It is one of the villages within Mukim Sengkurong.

Villages of Brunei
A village (Malay: kampung or kampong) is the third and lowest administrative division of Brunei. It is headed by a village head (ketua kampung). Several villages are grouped together to form a mukim. A village is generally the traditional rural settlement, in particular in the sense of a kampong or Malay traditional village, but it may also be an urbanised settlement within or near the capital city or a town, or part of the public housing estates. The population varies from hundreds to a few thousands.
Sniper Elite III
Sniper Elite III is a 2014 third-person tactical shooter stealth video game developed and published by Rebellion Developments. The game is a prequel to its 2012 predecessor Sniper Elite V2, and is the third installment in the Sniper Elite series. A direct sequel, Sniper Elite 4, was released in 2017.

Sniper Elite III is set around three years prior to the events of V2, following the exploits of OSS officer Karl Fairburne as he participates in the North African conflict during World War II, and works to stop the development of a deadly new weapon and eliminate the renegade Nazi commander responsible for it.

Third-person (video games)
In video games, third-person (also spelled third person) is a graphical perspective rendered from a fixed distance behind and slightly above the player character. This viewpoint allows players to see a more strongly characterized avatar and is most common in action games and action adventure games. Games with this perspective often make use of positional audio, where the volume of ambient sounds varies depending on the position of the avatar.