hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Algebraically closed field
In mathematics, a field F is algebraically closed if every non-constant polynomial with coefficients in F has a root in F. In other words, a field is algebraically closed if the fundamental theorem of algebra holds for it.  For example, the field of real numbers is not algebraically closed because the polynomial  has no real roots, while the field of complex numbers is algebraically closed.

Every field  is contained in an algebraically closed field  and the roots in  of the polynomials with coefficients in  form an algebraically closed field called an algebraic closure of  Given two algebraic closures of  there are isomorphisms between them that fix the elements of

Algebraically closed fields appear in the following chain of class inclusions:

rngs ⊃ rings ⊃ commutative rings ⊃  integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ euclidean domains ⊃ fields ⊃ algebraically closed fields

Algebraic number field
In mathematics, an algebraic number field (or simply number field) is an extension field  of the field of rational numbers  such that the field extension  has finite degree (and hence is an algebraic field extension).
Thus  is a field that contains  and has finite dimension when considered as a vector space over .

The study of algebraic number fields, that is, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory. This study reveals hidden structures behind the rational numbers, by using algebraic methods.
Royal Canadian Mint
The Royal Canadian Mint (French: Monnaie royale canadienne) is the mint of Canada and a Crown corporation, operating under an act of parliament referred to as the Royal Canadian Mint Act. The shares of the mint are held in trust for the Crown in right of Canada.

The mint produces all of Canada's circulation coins, and manufactures circulation coins on behalf of other nations. The mint also designs and manufactures precious and base metal collector coins; gold, silver, palladium, and platinum bullion coins; medals, as well as medallions and tokens. It further offers gold and silver refinery and assay services.

The mint serves the public's interest but is also mandated to operate "in anticipation of profit" (i.e., to function in a commercial manner without relying on taxpayer support to fund its operations). Like private-sector companies, the mint has a board of directors consisting of a chair, the president and CEO of the mint, and eight other directors.

Royal Australian Mint
The Royal Australian Mint  is the national mint of Australia, and the primary production facility for the country’s circulating coins. The mint is a Commonwealth Government entity operating within the portfolio of the Treasury, and is situated in the Australian capital city of Canberra, in the suburb of Deakin. The current facility was opened in 1965 by Prince Philip, Duke of Edinburgh.

Before the opening of the Australian Mint, Australian coins were struck at the Sydney Mint, Melbourne Mint and Perth Mint. As such, the Royal Australian Mint was the first mint in Australia to be independent of the British Royal Mint, in the United Kingdom, which was a British government entity. (Of the three older Australian mints, only Perth Mint has remained; it was a subsidiary of the UK Royal Mint until 1970.)
Gerry Studds
Gerry Eastman Studds (/ˈɡɛri/ GHERR-ee; May 12, 1937 – October 14, 2006) was an American politician from Massachusetts who served as a Democratic member of the United States House of Representatives from 1973 until 1997. He was the first member of Congress to be openly gay. In 1983, Studds was censured by the House for having sex with a 17-year-old page.

Mario Biaggi
Mario Biaggi (October 26, 1917 – June 24, 2015) was an American politician, attorney, and police officer. He served ten terms as a member of the United States House of Representatives from New York from 1969 to 1988.

Prior to his political career, Biaggi became one of the most decorated officers in NYPD history; he killed two criminals who attacked him and was injured 11 times as an officer. He then became an attorney at 49 years of age. First elected a U.S. Representative as a Democrat from the Bronx in 1968, Biaggi was subsequently re-elected nine times, seven times with more than 90% of the vote.

In 1987 and 1988, he was convicted in two trials of receipt of unlawful gratuities, and, facing the prospect of expulsion from the House, he resigned from Congress in 1988.
Cocopah
The Cocopah (Cocopah: Xawiƚƚ Kwñchawaay) are Native Americans who live in Baja California, Mexico, and Arizona, United States.

In the United States, Cocopah people belong to the federally recognized Cocopah Tribe of Arizona.

Mohave people
Mohave or Mojave (Mojave: Aha Makhav) are a Native American people from the Colorado River region of the Mojave Desert in Arizona, California, and Nevada. They are enrolled in the federally recognized tribes, the Fort Mojave Indian Tribe of Arizona, California & Nevada and the Colorado River Indian Tribes of the Colorado River Indian Reservation.

Their Mojave language belongs to the Yuman language family.

The original Colorado River and Fort Mojave reservations were established in 1865 and 1870. Both reservations include substantial senior water rights for the Colorado River.
Gary Moeller
Gary Oscar Moeller (/ˈmoʊlər/; January 26, 1941 – July 11, 2022) was an American football coach best known for being head coach at the University of Michigan from 1990 to 1994. During his five seasons at Michigan, he won 44 games, lost 13 and tied 3 for a winning percentage of .758. In Big Ten Conference play, his teams won 30 games, lost 8, and tied 2 for a winning percentage of .775, and won or shared conference titles in 1990, 1991 and 1992. He left Michigan in 1995 following a drunken incident. Moeller also coached in professional football and was the head coach of the Detroit Lions for part of the 2000 season. He was the father of former Cleveland Browns offensive line coach Andy Moeller.

Illinois Fighting Illini football
The Illinois Fighting Illini football program represents the University of Illinois Urbana-Champaign in college football at the NCAA Division I Football Bowl Subdivision (formerly Division I-A) level. The Fighting Illini are a founding member of the Big Ten Conference, and have played their home games at Gies Memorial Stadium in Champaign, Illinois since 1923. The Fighting Illini are currently led by head coach Bret Bielema.

Illinois claims 15 Big Ten championships, ranking 4th-most among conference members, and 5 national championships, ranking 13th-most among NCAA Division 1 programs.  Illinois has had 27 Consensus All-Americans, and 15 former Illini have been inducted into the College Football Hall of Fame; in the Pro Football Hall of Fame, 6 former Illini have been inducted. Illinois has three trophy rivalries against Northwestern, Purdue, and Ohio State.
IMZ-Ural
IMZ-Ural Group Inc., more commonly known as Ural Motorcycles (Russian: Мотоциклы Урал, romanized: Motosikly Ural), is a multinational company involved in developing, manufacturing, and worldwide distribution of Ural sidecar motorcycles. Headquartered in Redmond, Washington, with assembly facilities in Petropavl, Kazakhstan, Ural is the oldest and one of the world's largest manufacturers of sidecar-equipped motorcycles.

BMW Motorrad
BMW Motorrad is the motorcycle brand and division of German automotive manufacturer, BMW. It has produced motorcycles since 1923, and achieved record sales for the fifth year in succession in 2015. With a total of 136,963 vehicles sold in 2015, BMW registered a growth of 10.9%  in sales in comparison with 2014.
In May 2011, the 2,000,000th motorcycle produced by BMW Motorrad was an R1200GS.
Gauleiter
A Gauleiter (German pronunciation: [ˈɡaʊlaɪtɐ] ⓘ) was a regional leader of the Nazi Party (NSDAP) who served as the head of a Gau or Reichsgau. Gauleiter was the third-highest rank in the Nazi political leadership, subordinate only to Reichsleiter and to the Führer himself. The position was effectively abolished with the fall of the Nazi regime on 8 May 1945.

Gau March of Brandenburg
The Gau March of Brandenburg (German: Mark Brandenburg) was formed in March 1933 initially under the name Gau Electoral March (German: Kurmark) in Nazi Germany as a district within the Free State of Prussia. In January 1939, Kurmark was renamed March of Brandenburg. The Gau was dissolved in 1945, following Allied Soviet occupation of the area and Germany's formal surrender. After the war, the territory of the former Gau became part of the state of Brandenburg in East Germany except for areas beyond the Oder-Neisse line, which were given to the Polish People's Republic. Most of its territory is now divided between Germany's State of Brandenburg and Poland's Lubusz Voivodeship.
Stansfield, West Yorkshire
Stansfield (/ˈstænsfiːld/ STANSS-feeld) is a place in the civil parish of Todmorden, in the Calderdale district, in West Yorkshire, England, which gave its name to Stansfield Hall, Stansfield Hall Railway Station, and an electoral ward in Todmorden, Calderdale.

Thomas Wolryche Stansfeld
Brigadier-General Thomas Wolryche Stansfeld CMG DSO (English: /ˈwʊlrɪtʃ ˈstænsfiːld/ WUUL-ritch STANSS-feeld; 30 June 1877 – 22 February 1935) was a British army officer who served in the Boer War (1899–1902) and World War I, seeing action at the First Battle of Ypres and Battle of Passchendaele and other battles.
East Haven, Connecticut
East Haven is a town in New Haven County, Connecticut, United States. As of the 2020 census, the town population was 27,923. The town is located 3 miles (5 km) east of New Haven, and is part of the South Central Connecticut Planning Region. East Haven is 35 miles (56 km) from Hartford, 82 miles (132 km) from New York City, 99 miles (159 km) from Providence, Rhode Island, and 140 miles (230 km) from Boston.

Meriden, Connecticut
Meriden (/ˈmɛərədɪn/ MAIR-ə-din) is a city in New Haven County, Connecticut, United States, located halfway between the regional cities of New Haven and Hartford. The city is part of the South Central Connecticut Planning Region. In 2020, the population of the city was 60,850.
Torneo cibernetico
A torneo cibernetico is a multi-man professional wrestling elimination match that was created and primarily used in Mexican lucha libre professional wrestling promotions, especially in Consejo Mundial de Lucha Libre (CMLL). The match format sees two teams of varying sizes face off against each other. It uses standard lucha libre tag team rules with elimination occurring with a pinfall, submission, disqualification and count out and allows a wrestler to enter the match when their tag team partner exits the ring as well as when they tag out. A special 'batting' order system is sometimes used in which the wrestlers are given a specific order and may only tag in and out in this order. If two or more men from the same team remain, they must face each other to determine one individual winner.

Batiri
The Batiri are a professional wrestling alliance who perform on the independent circuit. They are best known for their time in the now-defunct Chikara promotion. The team includes Kodama and Obariyon, who work under face paint with the wrestling characters of demons, and Kobald, who performs under a goblin mask. Both Kodama's and Obariyon's ring names come from Japanese folklore from the characters of Kodama (木霊, Kodama) and Obariyon (おばりよん, Obariyon), while Kobald is named after the German word for goblin. All three men were trained at Chikara's Wrestle Factory by then head trainers Claudio Castagnoli and Mike Quackenbush. They have also made appearances for promotions like Beyond Wrestling, Collective League of Adrenaline Strength and Honor (CLASH), STAR Pro-Wrestling, Wrestling is Fun! (WiF!), and Absolute Intense Wrestling (AIW).
Milwaukee Wave
The Milwaukee Wave are an American professional indoor soccer team based in Milwaukee, Wisconsin, that competes in the Major Arena Soccer League (MASL). Founded in 1984, they have been the oldest continuously operating professional indoor soccer team in the United States and are seven-time league champions, most recent being the 2018–19 champions of the MASL.

The team plays their games at the UW–Milwaukee Panther Arena. The team colors are black and yellow. The team has won seven league championships in their history, three in the NPSL, three in the MISL, and one in the MASL.

Memphis Storm
The Memphis Storm was an American soccer team based in Memphis, Tennessee which existed from 1986 to 1994. They underwent several names changes including the Rogues, the Survivors, the United Express and finally the Jackals. They played in the American Indoor Soccer Association, and the Sunbelt Independent Soccer League, which later came to be known as the United States Interregional Soccer League.
Wayzata, Minnesota
Wayzata (/waɪˈzɛtə/ wy-ZET-ə) is a city in Hennepin County, Minnesota, United States. The population was 4,434 at the 2020 census. A suburb of the Twin Cities, Wayzata is located about 9 miles (14 km) west of Minneapolis along the northern shore of Lake Minnetonka, the state's ninth-largest lake.

Nicknamed "The Gateway to Lake Minnetonka," Wayzata is known for its upscale shopping and restaurant district along the lakeshore. Given its relative proximity to Minneapolis, the city is frequented by boaters, sailors, and visitors during the summer months.

Coon Rapids, Minnesota
Coon Rapids is a northern suburb of Minneapolis, and the second-largest city by population in Anoka County, Minnesota, United States. The population was 63,599 at the 2020 census, making it Minnesota's 15th-largest city and the seventh-largest Twin Cities suburb.
Wenatchee Mountains
The Wenatchee Mountains are a range of mountains in central Washington State in the United States of America. A major subrange of the Cascade Range, extending east 50 miles (80 km) from the Cascade crest, the Wenatchee Mountains separate the drainage basins of the Yakima and the Wenatchee rivers. The crest of the range forms part of the boundary between Chelan and Kittitas counties.

Cle Elum River
The Cle Elum River is a tributary of the Yakima River, approximately 28 miles (45 km) long in the U.S. state of Washington. A Northern Pacific Railway station at the future site of the city of Cle Elum, Washington was named Clealum after the Kittitas name Tie-el-Lum, meaning "swift water", referring to the Cle Elum River. In 1908, Clealum was altered to Cle Elum. This spelling came to be used for the river as well. Some maps in the 1850s also have the river labeled as Samahma River.
Liquidambar styraciflua
Liquidambar styraciflua, commonly known as the American sweetgum among other names, is a deciduous tree in the genus Liquidambar native to warm temperate areas of eastern North America and tropical montane regions of Mexico and Central America. Sweetgum is one of the main valuable forest trees in the southeastern United States, and is a popular ornamental tree in temperate climates. It is recognizable by the combination of its five-pointed star-shaped leaves (similar to maple leaves) and its hard, spiked fruits. It is currently classified in the plant family Altingiaceae, but was formerly considered a member of the Hamamelidaceae.

Quercus shumardii
Quercus shumardii, the Shumard oak, spotted oak, Schneck oak, Shumard red oak, or swamp red oak, is one of the largest of the oak species in the red oak group (Quercus section Lobatae). It is closely related to Quercus buckleyi (Texas red oak), Quercus texana (Nuttall's red oak), and Quercus gravesii (Chisos red oak).
Manumatic
The modern usage of the automotive term manumatic denotes an automatic transmission that allows the driver to select a specific gear, typically using paddle-shifters, steering wheel-mounted push-buttons, or "+" and "-" controls on the gear selector.

In the 1950s, the Automotive Products company in the United Kingdom produced an automated clutch system for automobiles called the Manumatic. This system was installed in cars with a manual transmission, allowing them to be driven without needing to use a clutch pedal.

ZF 5HP transmission
5HP is ZF Friedrichshafen AG's trademark name for its 5-speed automatic transmission models (5-speed transmission with Hydraulic converter and Planetary gearsets) for longitudinal engine applications, designed and built by ZF's subsidiary in Saarbrücken.
Baoshan, Yunnan
Baoshan (Chinese: 保山; pinyin: Bǎoshān ⓘ; Burmese: ပေါက်ရှန်), historically also Yongchang (Chinese: 永昌; pinyin: Yǒngchāng), is a prefecture-level city in western Yunnan Province, People's Republic of China. Baoshan is the second-biggest metropolitan area in western Yunnan after Dali.

Mangshi
Mangshi (Chinese: 芒市; Wade–Giles: Mangshih; Tai Nüa: ᥝᥥᥒᥰ ᥛᥫᥒᥰ ᥑᥩᥢᥴ; Jingpho: Mangshi Myu), former name Luxi (潞西), is a county-level city and the seat of Dehong Dai and Jingpo Autonomous Prefecture in western Yunnan province, China. Mangshi has an area of 2,900.91 km2 (1,120.05 sq mi), with an urban area of 18.66 km2 (7.20 sq mi). Han Chinese, Dai people (Tai Nuea branch) and Jingpo people (Zaiwa branch) are the major ethnic groups. Luxi County was established in 1949, and became a county-level city in 1996.
American Library Association
The American Library Association (ALA) is a nonprofit organization based in the United States that promotes libraries and library education internationally. It is the oldest and largest library association in the world.

Isadore Gilbert Mudge
Isadore Gilbert Mudge (March 14, 1875 – May 16, 1957) was ranked by the magazine American Libraries as one of the top 100 important leaders that libraries have had in the 20th century.  Mudge was a defining influence on what a contemporary reference librarian is and was essential for helping organize and promote reference books for use in helping patrons find information and answers to questions.

The only biography that exists of Isadore Gilbert Mudge is a dissertation written by Columbia student, John N. Waddell, in 1973.   In one portion he sums up what were her ideals, “Mudge’s professional concerns were not confined to the Columbia reference department….She was constantly concerned with the problems and tools bibliographical control in the widest possible area….but herself preached the gospel of cooperative bibliographic at home and abroad, by pen and by tongue.”
Seth-Peribsen
Seth-Peribsen (also known as Ash-Peribsen, Peribsen and Perabsen) is the serekh name of an early Egyptian monarch (pharaoh), who ruled during the Second Dynasty of Egypt (c. 2890 – c. 2686 BC). His chronological position within this dynasty is unknown and it is disputed who ruled both before and after him. The duration of his reign is also unknown.

Peribsen's name is unusual, in that Set, not Horus, was his patron deity. This goes against the Egyptian tradition of a king choosing the falcon-shaped deity Horus as his royal patron.

Peribsen's tomb was discovered in 1898 at Abydos. It was well preserved and showed traces of restoration undertaken during later dynastic periods.

Third Dynasty of Egypt
The Third Dynasty of ancient Egypt (Dynasty III) is the first dynasty of the Old Kingdom. Other dynasties of the Old Kingdom include the Fourth, Fifth and Sixth. The capital during the period of the Old Kingdom was at Memphis.
1992–93 UEFA Cup
The 1992–93 UEFA Cup was the 22nd season of Europe's then-tertiary club football tournament organised by UEFA. The final was played over two legs at Westfalenstadion, Dortmund, Germany, and at Stadio Delle Alpi, Turin, Italy. The competition was won by Italian club Juventus, who beat Borussia Dortmund of Germany by an aggregate result of 6–1, to claim their third UEFA Cup title.

Juventus became the first club to win the UEFA Cup three times, and registered a record score for a two-legged UEFA Cup final. Due to the breakup of Yugoslavia and the international sanctions for the ongoing Yugoslav Wars, UEFA banned all Yugoslavian teams from competing. Slovenia, a former Yugoslav republic, was represented for the first time in the UEFA Cup, although Olimpija Ljubljana competed in its unofficial predecessor Inter-Cities Fairs' Cup in the late 1960s.

1990–91 UEFA Cup
The 1990–91 UEFA Cup was the 20th season of the UEFA Cup, the secondary club football competition organised by the Union of European Football Associations (UEFA). The final was played over two legs at San Siro, Milan, Italy, and at the Stadio Olimpico, Rome, Italy. The competition was won by Internazionale, who defeated fellow Italian team Roma by an aggregate result of 2–1 to claim their first UEFA Cup title.

For the second consecutive year, two Italian teams reached the final of the UEFA Cup, This was the first European title for Internazionale in 26 years, after their two consecutive European Cup triumphs in 1964 and 1965. This tournament also marked the return of English clubs, after a five-year ban resulting from the Heysel Stadium disaster in 1985.
North Carolina FC
North Carolina FC is an American professional soccer team in Cary, North Carolina, a suburb of Raleigh, and member of the United Soccer League system. Founded in 2006, the team was known as the Carolina Railhawks.

On December 6, 2016, the RailHawks announced a name change to North Carolina Football Club in pursuit of becoming a Major League Soccer franchise. The club's home attendance record had been broken earlier that year when 10,125 attended a match against West Ham United of the English Premier League.

On November 4, 2025, the club announced it was suspending operations pending an application to join the future USL Premier in 2028.

The team has played its home games at the 10,000-seat WakeMed Soccer Park since 2007. The team's colors are Atlantic blue, cardinal red, and Southern gold.

North Texas SC
North Texas Soccer Club is a professional soccer club that competes in MLS Next Pro, the third division of American soccer. The team is owned by, and operates as the reserve team of the Major League Soccer club FC Dallas. North Texas SC currently plays most home games at Texas Health Mansfield Stadium, located in Mansfield, Texas. Before the 2022 restructuring of MLS reserve teams, the team competed in USL League One as one of the league's founding members.
Community (Wales)
A community (Welsh: cymuned) is a division of land that forms the lowest tier of local government in Wales. Welsh communities are analogous to civil parishes in England but, unlike English parishes, communities cover the whole of Wales. There are 878 communities in Wales, with more than 730 having community and town councils.

Manordeifi
Manordeifi (Welsh: Maenordeifi) is a parish and community in the hundred of Cilgerran, in the northeast corner of Pembrokeshire, Wales. The population of the community in 2001 was 478. It has an elected community council and is part of the Cilgerran electoral ward for the purposes of elections to Pembrokeshire County Council.

In addition to scattered settlement, the parish contains the villages of Abercych and Newchapel (Welsh: Capelnewydd), and many listed buildings and structures.
Northwich
Northwich is a market town and civil parish in the Cheshire West and Chester borough of Cheshire, England. It lies on the Cheshire Plain, at the confluence of the rivers Weaver and Dane, 18 miles (29 km) east of Chester, 15 miles (24 km) south of Warrington, 19 miles (31 km) south of Manchester, 69 miles (111 km) north of Birmingham, and 36 miles (58 km) south-east of Liverpool. The population of the parish was 22,726 at the 2021 census.

The area around Northwich was exploited for its salt pans by the Romans, when the settlement was known as Condate. The town had been severely affected by salt mining and subsidence was historically a significant problem. Mine stabilisation work was completed in 2007.

Tarporley
Tarporley is a large village and civil parish in Cheshire, England. The civil parish also contains the village of Rhuddall Heath. Tarporley is bypassed by the A49 and A51 roads.

At the 2011 census, the population was 2,614.