hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Multiplicatively closed set
In abstract algebra, a multiplicatively closed set (or multiplicative set) is a subset S of a ring R such that the following two conditions hold:

,

for all .

In other words, S is closed under taking finite products, including the empty product 1.
Equivalently, a multiplicative set is a submonoid of the multiplicative monoid of a ring.

Multiplicative sets are important especially in commutative algebra, where they are used to build localizations of commutative rings.

A subset S of a ring R is called saturated if it is closed under taking divisors: i.e., whenever a product xy is in S, the elements x and y are in S too.

Empty product
In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question; when numbers are implied, it becomes one), just as the empty sum — the result of adding no numbers — is by convention equal to the additive identity (zero).

The term empty product is most often used in the above sense when discussing arithmetic operations. However, the term is sometimes employed when discussing set-theoretic intersections, categorical products, and products in computer programming.
Massachusetts House of Representatives' 3rd Middlesex district
Massachusetts House of Representatives' 3rd Middlesex district (or "3rd Middlesex") is an electoral district for the Massachusetts House of Representatives. Located in central Massachusetts, it comprises the towns of Hudson, Maynard and Stow (all of which are located in Middlesex County), as well as the town of Bolton (located in Worcester County). Democrat Kate Hogan of Stow has represented the district since 2013. She is running unopposed for re-election in the 2020 Massachusetts general election.

The current district geographic boundary overlaps with those of the Massachusetts Senate's Middlesex and Worcester district and Worcester and Middlesex district.

2020 Massachusetts elections
The 2020 Massachusetts general election was held on November 3, 2020, throughout Massachusetts. Primary elections were held on September 1, 2020.

At the federal level, all nine seats in the United States House of Representatives were up for election. Also contested was the United States Senate seat held by Ed Markey.

At the state level, all seats in the Massachusetts General Court (state legislature) were up for election.

To vote by mail, registered Massachusetts voters had to request a ballot by October 30, 2020. As of early October, some 504,043 voters had requested mail ballots.
Shaala Darpan
Shala Darpan is an ICT Programme of Ministry of Human Resource Development, Government of India that aims to provide mobile access to parents of students of Government and Government aided schools. This information can only be obtained about the students of government schools. The implementation of Shala Darpan Portal is with the Rajasthan Government Education Department.

Government of Rajasthan
The Government of Rajasthan is the supreme governing authority of the Indian state of Rajasthan and its 41 districts. It consists of an executive branch, led by the governor of Rajasthan, as well as judiciary and legislative branches. Jaipur is the capital of Rajasthan, and houses the Vidhan Sabha (legislative assembly) and the secretariat. There are various programs announced by the Government of Rajasthan.
Chabanmakhi
Chabanmakhi (Russian: Чабанмахи; Dargwa: Чабанмахьи) is a rural locality (a selo) in Karamakhinsky Selsoviet, Buynaksky District, Republic of Dagestan, Russia. The population was 1,083 as of 2010. There are 15 streets.

Buynaksky District
Buynaksky District  (Russian: Буйнакский район, Kumyk: Шура якъ) is an administrative and municipal district (raion), one of the forty-one in the Republic of Dagestan, Russia. It is located in the center of the republic. The area of the district is 1,842.09 square kilometers (711.23 sq mi). Its administrative center is the town of Buynaksk (which is not administratively a part of the district). As of the 2010 Census, the total population of the district was 73,402.
Herman Ouseley, Baron Ouseley
Herman George Ouseley, Baron Ouseley (24 March 1945 – 2 October 2024) was a British parliamentarian. Before becoming a member of the House of Lords he was an important figure in public authorities, including local councils, and was an adviser and reviewer of public services organisations with a particular focus on equality and diversity. He was at the forefront of challenging institutional racism in organisations and was an advocate on behalf of individuals from disadvantaged and deprived backgrounds.

Ouseley sat in the House of Lords as an crossbencher from 2001 until his retirement in 2019. He was also included in the 2003 list of "100 Great Black Britons".

Ouseley was a supporter of Millwall and Rangers.

Crossbencher
A crossbencher is a minor party or independent member of some legislatures, such as the Parliament of Australia. In the British House of Lords the term refers to members of the parliamentary group of non-political peers. They take their name from the crossbenches, between and perpendicular to the government and opposition benches, where crossbenchers sit in the chamber.
Patty Gasso
Patricia Marie Gasso (née Froehlich; born May 27, 1962) is an American softball coach for the Oklahoma Sooners and United States women's national softball team. She has been the head softball coach at the University of Oklahoma since 1995.  She has led the Sooners to eight national championships (2000, 2013, 2016, 2017, 2021, 2022, 2023, and 2024) and has compiled a career record of 1,567–361–2 and a winning percentage of .812. Gasso's son, DJ, has been an assistant coach for the Arkansas Razorbacks softball team since 2023.

2017 NCAA Division I softball tournament
The 2017 NCAA Division I softball tournament was held from May 18 through June 7, 2017, as the final part of the 2017 NCAA Division I softball season. The 64 participating NCAA Division I college softball teams were selected out of an eligible 293 teams on May 14, 2017. Thirty-two teams were awarded automatic bids as champions of their conferences, and the remaining 32 were selected at-large by the NCAA Division I softball selection committee. The tournament culminated with eight teams playing in the 2017 Women's College World Series at ASA Hall of Fame Stadium in Oklahoma City. Oklahoma would repeat as National Champions, defeating Florida in 2 games and 17 innings in the first game. Oklahoma became the lowest seeded team to ever win the National Championship, winning as the 10 seed.
1999–2000 Red Stripe Bowl
The 1999–2000 Red Stripe Bowl was the 26th season of what is now the Regional Super50, the domestic limited-overs cricket competition for the countries of the West Indies Cricket Board (WICB). It ran from 27 October to 7 November 1999.

Eight teams contested the competition – the six regular teams of West Indian domestic cricket (Barbados, Guyana, Jamaica, the Leeward Islands, Trinidad and Tobago, and the Windward Islands), plus two invited international teams from the ICC Americas region (Bermuda and Canada). The tournament was impacted by rain, with three matches (including the final) being interrupted and another three (including a semi-final) being abandoned entirely. Jamaica eventually defeated the Leeward Islands in the final to win their sixth domestic one-day title. Leeward Islands batsman Sylvester Joseph led the tournament in runs, while Guyana's Neil McGarrell took the most wickets.

Result (cricket)
The result in a game of cricket may be a "win" for one of the two teams playing, or a "tie". In the case of a limited overs game, the game can also end with "no result" if the game cannot be finished on time (usually due to weather or bad light), and in other forms of cricket, a "draw" may be possible. Which of these results applies, and how the result is expressed, is governed by Law 16 of the laws of cricket.
Ingleton, County Durham
Ingleton is a village  and civil parish in County Durham, England. The population of the parish (which includes Headlam and Langton) as taken at the 2011 census was 420. It is situated about eight miles to the west of Darlington, and a short distance from the villages of Langton, Hilton and Killerby. The Church of St John the Evangelist in Ingleton was built in 1843 by Ignatius Bonomi and J.A. Cory., and is a Grade II listed building.

Headlam
Headlam is a hamlet and civil parish in County Durham, England. It lies to the west of Darlington. In 2021 the parish had a population of 41. The hamlet has 14 stone houses plus 17th-century Headlam Hall, now a country house hotel. The village is set around a village green with a medieval cattle-pound and an old stone packhorse bridge across the beck. Headlam is classed as Lower Teesdale and has views to the south as far as Richmond and to the Cleveland Hills in the east.

In the Imperial Gazetteer of England and Wales (1870–72) John Marius Wilson described Headlam:

HEADLAM, a township in Gainford parish, Durham: 7½ miles WNW of Darlington. Acres, 780. Real property, £1,216. Pop., 102. Houses, 21.
Stanley Couchman
Stanley Randall Couchman (10 August 1913 – 20 November 1992) was an English international rugby union player.

Couchman was born in London and attended Cranleigh School.

A second row forward, Couchman competed for Old Cranleighans and was a regular representative player with Surrey, making 45 appearances for the county. He was an England trialist and in 1938 toured with the British Lions to South Africa, where he played 11 matches. After retiring, Couchman became an administrator and served as president of Surrey RFU from 1958 to 1961, then had a term as Rugby Football Union president in 1978–79.

Couchman's son James was a Conservative member of parliament for Gillingham.

Rugby Football Union
The Rugby Football Union (RFU) is the national governing body for rugby union in England. It was founded in 1871, and was the sport's international governing body prior to the formation of what is now known as World Rugby (WR) in 1886. It promotes and runs the sport, organises international matches for the England national team, and educates and trains players and officials.

The RFU is an industrial and provident society owned by over 2,000 member clubs, representing over 2.5 million registered players, and forms the largest rugby union society in the world, and one of the largest sports organisations in England. It is based at Twickenham Stadium, London.

In September 2010 the equivalent women's rugby body, the Rugby Football Union for Women (RFUW), was able to nominate a member to the RFU Council to represent women's and girls' rugby. The RFUW was integrated into the RFU in July 2012.
29th Guldbagge Awards
The 29th Guldbagge Awards ceremony, presented by the Swedish Film Institute, honored the best Swedish films of 1993, and took place on 31 January 1994. The Slingshot directed by Åke Sandgren was presented with the award for Best Film.

Guldbagge Award for Best Film
The Guldbagge for Best Film is a Swedish film award presented annually by the Swedish Film Institute (SFI) as part of the Guldbagge Awards (Swedish: "Guldbaggen") to the best Swedish motion picture of the year.
Maria de Guadalupe, 6th Duchess of Aveiro
Dona Maria de Guadalupe of Lencastre y Cárdenas Manrique (Azeitao, Portugal 1630 – Madrid, Spain 1715), was a Portuguese noblewoman, notable as an heiress who funded Catholic missions and missionaries in Asia, the Pacific, and Africa.

Marquis of Torres Novas
The title Marquis of Torres Novas (in Portuguese Marquês de Torres Novas) was created by royal decree, dated from 27 March 1520, by King Manuel I of Portugal, to Dom John of Lencastre (1501–1571), eldest son of Infante George, Duke of Coimbra.

In 1535 the new King, John III, granted him the new title of Duke of Aveiro and, from then on, the title of Marquis of Torres Novas was allocated to the Duke of Aveiro's heir.
Perfect Day (Chris Whitley album)
Perfect Day is the sixth album by singer-songwriter and guitarist, Chris Whitley. It is his fifth studio album.

It is a full-length release of "quiet jazzy" cover versions of "love songs". The album was recorded as a trio and is subtitled "Featuring Billy Martin and Chris Wood". Martin and Wood are the rhythm section of Medeski Martin & Wood.

It was produced by Craig Street. The album was recorded live to half-inch two-track recorder by Danny Kopelson at 331⁄3 Recording in Brooklyn, New York.

This recording was also released in the Super Audio CD (SACD) format.

Super Audio CD
Super Audio CD (SACD) is an optical disc format for audio storage introduced in 1999. It was developed jointly by Sony and Philips Electronics and intended to be the successor to the compact disc (CD) format.

The SACD format allows multiple audio channels (i.e., surround sound or multichannel sound). It also provides a higher bit rate and longer playing time than a conventional CD.

An SACD is designed to be played on an SACD player. A hybrid SACD contains a Compact Disc Digital Audio (CDDA) layer and can also be played on a standard CD player.
Fatimah Asghar
Fatimah Asghar is a South Asian American poet, director and screenwriter. Co-creator and writer for the Emmy-nominated webseries Brown Girls, their work has appeared in Poetry, Gulf Coast, BuzzFeed Reader, The Margins, The Offing, Academy of American Poets, and other publications.

Asghar is a member of the Dark Noise Collective and a Kundiman Fellow. They received the Ruth Lilly and Dorothy Sargent Rosenberg Poetry Fellowship from the Poetry Foundation in 2017, and has been featured on the Forbes 30 Under 30 list.

Kundiman (nonprofit organization)
Kundiman is a nonprofit organization dedicated to writers and readers of Asian American literature. Among its services are readings, workshops, mentorship programs, writing intensives, as well as a poetry prize and an annual writing retreat, the Kundiman Retreat.
Bandon Marsh National Wildlife Refuge
Bandon Marsh National Wildlife Refuge is a U.S. National Wildlife Refuge on Oregon's coast. It is one of six National Wildlife Refuges comprising the Oregon Coast National Wildlife Refuge Complex and is renowned among bird watchers for being able to view rare shorebirds including ruff, Hudsonian godwit, and Mongolian plover.
The refuge was last expanded in 1999, it now has 889 acres (3.60 km2) in two units:  Bandon Marsh and Ni-les'tun.

National Wildlife Refuge
The National Wildlife Refuge System is a system of protected areas of the United States managed by the United States Fish and Wildlife Service, an agency within the Department of the Interior. The National Wildlife Refuge System is the system of public lands and waters set aside to conserve America's fish, wildlife, and plants.
Nuris Arias
Nuris Arias Doñé (born May 20, 1973, in San Cristobal) is a retired volleyball player from the Dominican Republic, who won the gold medal with the women's national team at the 2003 Pan American Games in her home town of Santo Domingo, Dominican Republic. She was inducted into the Dominican Republic Hall of Fame in 2022.

San Cristóbal Province
San Cristóbal (Spanish pronunciation: [ˈsaŋ kɾisˈtoβal]) is a province in the southern region of Dominican Republic, located west of the capital Santo Domingo. With approximately 690,000 inhabitants (2022), it is the fourth most populated province in the country, only behind Santo Domingo, Santiago and the National District. It borders the provinces Monseñor Nouel (north), Monte Plata (northeast), Santo Domingo (east), Peravia (west) and San José de Ocoa (northwest). The Caribbean Sea borders the province to the south. The provincial capital is the city of San Cristóbal.

It was originally named Trujillo after the dictator Rafael Leónidas Trujillo, taking its present name after his assassination in 1961. It included what is now Monte Plata Province until 1992. The provincial capital is San Cristóbal.
The Old Man and the Sea (1990 film)
The Old Man and the Sea is a 1990 American-British adventure drama television film directed by Jud Taylor and written by Roger O. Hirson, based on the 1952 novella of the same name by Ernest Hemingway. The film stars Anthony Quinn, Gary Cole, Patricia Clarkson, and Joe Santos. It received mixed reviews and was nominated for three Primetime Creative Arts Emmy Awards.

Roger O. Hirson
Roger Overholt Hirson (May 5, 1926 – May 27, 2019) was an American dramatist and screenwriter best known for his books of the Broadway musicals, Pippin, for which he was nominated for a Tony Award, and Walking Happy. He contributed extensively for original television anthology series episodes since the 1950s and also wrote the screenplays or stories for several prominent films such as The Bridge at Remagen (1969).
Hucheshwar Gurusidha Mudgal
Hucheshwar Gurusidha Mudgal (2 September 1899, Hubli-19??)  was an Indian political activist who became prominent in Marcus Garvey's Universal Negro Improvement Association working on the Daily Negro Times and Negro World. Born in India, he arrived in New York City in 1920, where he stayed for seventeen years.

He was educated at City College of New York and Columbia University where he gained an M.A.

He returned to India in 1937 where he became a member of parliament for the Congress Party, but was forced to resign in a corruption scandal in 1951. He published an article about Bal Gandharva in The Times of India in 1967.

Bal Gandharva
Narayan Shripad Rajhans, popularly known as Bal Gandharva, (26 June 1888 – 15 July 1967) pronunciationⓘ was a famous Marathi singer and stage actor. He was known for his roles as female characters in Marathi plays, since women were not allowed to act on stage during his time.

Bal Gandharva got his name after a singing performance in Pune. Lokmanya Tilak, a social reformer and a freedom fighter of the Indian independence movement was in the audience, and after the performance, reportedly patted Rajhans on the back and said that Narayan was a "Bal Gandharva" (lit. Young Gandharva).
Cheryll Greene
Cheryll Y. Greene (December 20, 1943 – December 19, 2013) was an American editor and scholar. Her work focused on history, culture, and social justice issues. She served as executive editor of Essence magazine and was involved in major projects about the life and times of Malcolm X.

Between 1979 and 1985, Greene used Essence, a fashion magazine for African-American women, as a platform for publication of work about the African diaspora. While at the Institute for Research in African-American Studies (IRAAS) at Columbia University between 2001 and 2004, she was managing editor of the Malcolm X Project, as well as managing editor of Souls, an African-American studies journal. At IRAAS, she collaborated with Manning Marable in developing and conducting oral history interviews with associates of Malcolm X. Greene was a curatorial and research consultant for the 2005 exhibition Malcolm X: A Search for Truth at The New York Public Library's Schomburg Center for Research in Black Culture.

Alexis Pauline Gumbs
Alexis Pauline Gumbs (born 1982) is an American writer, independent scholar, poet, activist and educator based in Durham, North Carolina. Gumbs writes about and speaks about the lives and issues affecting queer women of color  and has been described by Lea Hulsen of the German academic journal, KULT_Online, as a “Black Feminist love evangelist,”. Gumbs describes herself as a "Queer Black Troublemaker" and "aspirational cousin to all sentient beings."  In her experimental triptych -- Spill, M Archive, and Dub—Gumbs explores the implications of humanity’s struggle with ecological disruption and Black feminist theory and refusals.
Philip Lange
Frantz Philip Nicolai Lange (31 March 1756 – 28 March 1805) was a Danish architect and master mason. He made a significant contribution to the rebuilding of Copenhagen in the years after the Copenhagen Fire of 1795. Most of his buildings have been listed on the Danish registry of protected buildings and places.

Sankt Peders Stræde
Sankt Peder Stræde is a street in central Copenhagen, Denmark. It runs from Nørregade to  Jarmers Plads, crossing Larsbjørnsstræde, Teglgårdsstræde and Larslejsstræde on the way.  The eponymous St. Peter's Church is located at the beginning of the street, on the corner with Nørregade. Most of its other buildings date from the years after the Copenhagen Fire of 1795. Part of Copenhagen's Latin Quarter, the street is home to several well-known restaurants and shops.
Conditional variance swap
A conditional variance swap is a type of variance swap or swap derivative product that allows investors to take exposure to volatility in the price of an underlying security but only while the underlying security is within a pre-specified price range.  This instrument can be useful for hedging complex volatility exposures, making a bet on the volatility levels contained in the skew of the underlying security's price, or  buying/selling variance at more attractive levels given a view on the underlying security.

Volatility (finance)
In finance, volatility (usually denoted by "σ") is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns.

Historic volatility measures a time series of past market prices.  Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option).
Hollows Grove
Hollows Grove is a 2014 independent horror film and the feature film directorial debut of Craig Efros. It was released as a digital download on 21 October 2014 and stars Matthew Carey as a filmmaker that decides to create a documentary centering upon a ghost hunting team, only to find that this could be the last thing he ever does.

Lance Henriksen
Lance Henriksen (born May 5, 1940) is an American actor. He is known for his roles in various science fiction, action and horror genre productions, including Bishop in the Alien film franchise and Frank Black in the television series Millennium (1996–99) and The X-Files (1999).

He has also done extensive voice work, including the Disney film Tarzan (1999) and the video games Gun (2005), Call of Duty: Modern Warfare 2 (2009) and BioWare's Mass Effect trilogy (2007–2012). Other film credits include The Right Stuff (1983), The Terminator (1984), Hard Target (1993), Color of Night (1994), The Quick and the Dead (1995), Powder (1995), Scream 3 (2000), Appaloosa (2008), and Falling (2020).

Henriksen was nominated for three Golden Globe Awards for his role on Millenium, and won a Saturn Award (out of four total nominations) for his performance in Hard Target. In 2021, he was nominated for a Canadian Screen Award for Best Actor for Falling.
Laura Swaan Wrede
Major General Laura Maria Swaan Wrede, née Swaan (born 16 August 1964) is a Swedish Army officer. She served as the Chief of Home Guard between 2022 and 2026. She previously served as regimental commander of the Life Guards between 2017 and 2020 (she was the first female commander of the Life Guards) and as the Deputy Chief of Army from 2020 to 2022.

United Nations Medal
A United Nations Medal is an international decoration awarded by the United Nations (UN) to the various world countries members for participation in joint international military and police operations such as peacekeeping, humanitarian efforts, and disaster relief. The medal is ranked in militaries and police forces as a service medal. The United Nations awarded its first medal during the Korean War (1950–1953).  Since 1955, many additional United Nations medals have been created and awarded for participation in various United Nations missions and actions around the world.