hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Generalized Cohen–Macaulay ring
In algebra, a generalized Cohen–Macaulay ring is a commutative Noetherian local ring  of Krull dimension d > 0 that satisfies any of the following equivalent conditions:

For each integer , the length of the i-th local cohomology of A is finite:
.

where the sup is over all parameter ideals  and  is the multiplicity of .

There is an -primary ideal  such that for each system of parameters  in ,

For each prime ideal  of  that is not ,  and  is Cohen–Macaulay.

The last condition implies that the localization  is Cohen–Macaulay for each prime ideal .

A standard example is the local ring at the vertex of an affine cone over a smooth projective variety. Historically, the notion grew up out of the study of a Buchsbaum ring, a Noetherian local ring A in which  is constant for -primary ideals ; see the introduction of.

Primary ideal
In mathematics, specifically commutative algebra, a proper ideal  of a commutative ring  is said to be primary if whenever  is an element of  then  or  is also an element of , for some . For example, in the ring of integers ,  is a primary ideal if  is a prime number.

The notion of primary ideals is important in commutative ring theory because every ideal of a Noetherian ring has a primary decomposition, that is, can be written as an intersection of finitely many primary ideals. This result is known as the Lasker–Noether theorem. Consequently, an irreducible ideal of a Noetherian ring is primary.

Various methods of generalizing primary ideals to noncommutative rings exist, but the topic is most often studied for commutative rings. Therefore, the rings in this article are assumed to be commutative rings with identity.
Iwai Hanshirō VIII
Iwai Hanshirō VIII (岩井半四郎 (8代目), October 2, 1829 – February 19, 1882) was a Japanese kabuki performer, known both for his own work and for his place in the lineage of a family of kabuki actors.  
He was the son of Iwai Hanshirō VII.

Iwai Hanshirō was a stage name with significant cultural and historical connotations.

In the conservative Kabuki world, stage names are passed from father to son in formal system which converts the kabuki stage name into a mark of accomplishment. This actor assumed the mantle of his father's stage name in 1872.

Lineage of Iwai stage names

Iwai Hanshirō I (1652–1699)

Iwai Hanshirō II (d. 1710)

Iwai Hanshirō III (1698–1760)

Iwai Hanshirō IV (1747–1800)

Iwai Hanshirō V (1776–1847)

Iwai Hanshirō VI (1799–1836)

Iwai Hanshirō VII (1804–1845)

Iwai Hanshirō VIII (1829–1882)

Iwai Hanshirō IX (1882–1945)

Iwai Hanshirō X (1927-2011)

Kabuki
Kabuki (歌舞伎; Japanese pronunciation: [ka.bɯ.kʲi]) is a classical form of Japanese theatre, mixing dramatic performance with traditional dance. Kabuki theatre is known for its heavily stylised performances, its glamorous, highly decorated costumes, and for the elaborate kumadori make-up worn by some of its performers.

Kabuki is thought to have originated in the early Edo period, when the art's founder, Izumo no Okuni, formed a female dance troupe that performed dances and light sketches in Kyoto. The art form later developed into its present all-male theatrical form after women were banned from performing in kabuki theatre in 1629. Kabuki developed throughout the late 17th century and reached its zenith in the mid-18th century.

In 2005, kabuki theatre was proclaimed by UNESCO as an intangible heritage possessing outstanding universal value. In 2008, it was inscribed in the UNESCO Representative List of the Intangible Cultural Heritage of Humanity.
Seyyid Abdullah Pasha
Seyyid Abdullah Pasha (also known as Boynueğri Seyyid Abdullah Pasha "Seyyid Abdullah Pasha the Crooked-neck"; died March 1761, Aleppo) was an Ottoman statesman who served as grand vizier from 1747 to 1750. He also served as the Ottoman governor of Cyprus (1745–46, again in 1746–47), Rakka (1746), Konya (1750), Bosnia (1750–51), Egypt (1751–52), Diyarbekir (1752–60), and Aleppo (1760).

Abdullah Pasha was born in Kirkuk, the son of Blond Seyyid Hasan-aga, who served as grand sheyhulislam of the Ottoman Empire before him. He attended the Enderun palace school as a youth and became a vizier in December 1745.

He died in office as governor of Aleppo in March 1760.

Diyarbekir Eyalet
The Eyalet of Diyarbekir (Arabic: إيالة ديار بكر; Ottoman Turkish: ایالت دیاربكر, romanized: Eyālet-i Diyār-i Bekr) was an eyalet of the Ottoman Empire. Its reported area in the 19th century was 20,332 square miles (52,660 km2), slightly larger than the original Abbasid province in Upper Mesopotamia. In 1846 it was succeeded by the Kurdistan Eyalet.
132nd Wing
The 132nd Wingis a United States Air Force unit assigned to the Iowa Air National Guard and located at Des Moines Air National Guard Base, Iowa. After having operated manned fighter aircraft for all of its prior history, the wing was equipped with the MQ-9 Reaper unmanned aerial vehicle in 2013.

Tactical Air Command
Tactical Air Command (TAC) is an inactive United States Air Force organization. It was a Major Command of the United States Air Force, established on 21 March 1946 and headquartered at Langley Air Force Base, Virginia. It was inactivated on 1 June 1992 and its personnel and equipment absorbed by Air Combat Command (ACC).

Tactical Air Command was established to provide a balance between strategic, air defense, and tactical forces of the post–World War II U.S. Army Air Forces followed by, in 1947, the U.S. Air Force. In 1948, the Continental Air Command assumed control over air defense, tactical air, and air reserve forces. After two years in a subordinate role, Tactical Air Command (TAC) was established as a major command.

In 1992, after assessing the mission of TAC and to accommodate a decision made regarding Strategic Air Command (SAC), Headquarters United States Air Force deactivated TAC and incorporated its resources into the newly created ACC.
Wyndham College
Wyndham College is a public senior secondary school located at Nirimba Fields, New South Wales, Australia.

Established in 1999, its intake of students comes from three surrounding high schools: Quakers Hill High School, Riverstone High School, and Seven Hills High School. With Wyndham College, they make the Nirimba Collegiate Group of Schools. The Collegiate Group of Schools all operate independently of each other, but the four principals work closely together.

The college is situated on the Nirimba Education Precinct, co-located within: the University of Western Sydney, Blacktown, Western Sydney Institute of TAFE – Nirimba College, and St John Paul II Catholic College, Senior Campus.

Visual artworks completed by students from the college are regularly nominated and featured in Art Express.

Seven Hills, New South Wales
Seven Hills is a suburb in the Greater Western Sydney region of Sydney, in the state of New South Wales, Australia, located 33 kilometres (21 mi) North West of the Sydney central business district. Seven Hills is within the local government areas of the City of Parramatta and Blacktown City councils.
Gigamacro
A gigapixel macro image is a digital image bitmap composed of one billion (109) pixels (picture elements), or 1000 times the information captured by a 1 megapixel digital camera. Creating such high-resolution images involves making mosaics (image stitching) of a large number of high-resolution digital photographs which are then combined into a single image.

Gigapixel macro images are made by 'stacking' a number of photographs together in order to increase the depth of field and then stitching the resulting images together in  a technique known as 'stack and stitch'. Such images are usually very large in size and cannot be easily viewed.  To make such images accessible, they are converted using tiled image techniques so that they may be viewed in a web browser. Such techniques are familiar in everyday use in e.g. Google Maps.

Tile-based video game
A tile-based video game, or grid-based video game, is a type of video game where the playing area consists of small square (or, much less often, rectangular, parallelogram, or hexagonal) graphic images referred to as tiles laid out in a grid. That the screen is made of such tiles is a technical distinction, and may not be obvious to people playing the game. The complete set of tiles available for use in a playing area is called a tileset. Tile-based games usually simulate a top-down, side view, or 2.5D view of the playing area, and are almost always two-dimensional.

Much video game hardware from the late 1970s through the mid-1990s has native support for displaying tiled screens with little interaction from the CPU.
Pinchas Mordechai Teitz
Rabbi Pinchas Mordechai Teitz (1908–1995) was a rabbi, teacher, author, and innovator in creating a modern Torah community in Elizabeth, New Jersey. He excelled in his family's tradition of caring for Jews across the globe in any challenges they faced. A mikvah he built in 1938, a day school he founded in 1941 that grew to more than 900 students, adult education courses that he initiated, the welcome he gave to displaced persons after WWII and to Jews who came from Russia, all became a model for other leaders to implement in their cities and towns.

Mikveh
A mikveh (pronounced [/ˈmik.ve/]; Hebrew: מִקְוֶא, romanized: miqveʾ, lit. 'a gathering [of water]'; pl. mikve'ot or mikvot) or mikvah (IPA: [/miqˈwaː/]) is a bath used during ritual immersion in Judaism to achieve ritual purity.

In Orthodox Judaism, these regulations are steadfastly adhered to; consequently, the mikveh is central to an Orthodox Jewish community. Conservative Judaism also formally holds to the regulations. The existence of a mikveh is considered so important that, according to Halakha, a Jewish community is required to construct a kosher mikveh even before building a synagogue, and must go to the extreme of selling Torah scrolls, or even a synagogue if necessary, to provide funding for its construction.
Fred Fortin
Fred Fortin (born Joseph Antoine Frédéric Fortin Perron on 5 May 1971 in Dolbeau-Mistassini, Quebec) is a Canadian rock singer-songwriter. Formerly associated with the bands Galaxie, Gros Mené and Les Breastfeeders, he has also released several solo albums. His 2009 album Plastrer la lune was a longlisted nominee for the 2010 Polaris Music Prize.

In 2007, he also collaborated with Jean-Philippe Fréchette of Navet Confit, Simon Proulx of Les Trois Accords and Vincent Peake of Groovy Aardvark in the supergroup Vauvandalou, who released the one-off single "0.99$" through Bande à part and Radio-Canada's Le Fric Show.

Le Fric Show
Le Fric Show is a Canadian television series, which airs on Radio-Canada. Hosted by Marc Labrèche, the series airs a satirical mix of advocacy journalism and entertainment segments. The series has some similarities to Labrèche's earlier La Fin du monde est à 7 heures.

The show first aired in 2006, and was renewed for a second season in 2007.

In 2007, the show collaborated with Bande à part to produce and present "0.99$", a one-off single and video by the Quebec supergroup Vauvandalou.
Actinodaphne menghaiensis
Actinodaphne menghaiensis is a species of tree belonging to the family Lauraceae. It is only known from Menghai County, Yunnan in the People's Republic of China.

This tree, growing to 8 m tall, is found in dense, humid forest. Whorls of five or six leaves, up to 40 cm long, are borne at the ends of branchlets. It is very similar to Actinodaphne obovata but can be distinguished by the glabrous branchlets, leaves and buds; and smaller fruits with more slender pedicels.

Glabrousness
Glabrousness (from Latin  glaber 'bald, hairless, shaved, smooth, etc.') is the technical term for a lack of hair, down, setae, trichomes, or other such covering. A glabrous surface may be a natural characteristic of all or part of a plant or animal, or be due to loss because of a physical condition, such as alopecia universalis in humans, which causes hair to fall out or not regrow.
Chalepensin
Chalepensin is a chemical compound of the furanocoumarin class.   Originally isolated in 1967 from fringed rue (Ruta chalepensis), from which it derives its name, it has also been found in other plants of the genus Ruta including common rue (Ruta graveolens) and mountain rue (Ruta montana).

Ruta
Ruta (commonly known as rue) is a genus of strongly scented evergreen subshrubs, 20–60 cm (8–24 in) tall, in the family Rutaceae, native to the Mediterranean region, Macaronesia and southwest Asia. About ten species are accepted in the genus. The most well-known species is Ruta graveolens (rue or common rue).

The leaves are bipinnate or tripinnate, with a feathery appearance, and green to strongly glaucous blue-green in colour. The flowers are yellow, with 4–5 petals, about 1 cm (1⁄2 in) across, and borne in cymes. The fruit is a 4–5-lobed capsule, containing numerous seeds.
Kim Roberts (filmmaker)
Kim Roberts (born 1970), A.C.E., is an American filmmaker who has worked primarily on documentaries as a film editor and writer. Roberts has a master's degree in documentary film production from Stanford University (1996). Her first credit as an editor was for Long Night's Journey into Day (2000), which was directed by Deborah Hoffmann and Frances Reid and that was nominated for the Academy Award for Best Documentary Feature. She was credited as both an editor and writer for Great Wall Across the Yangtze (2000), which was directed by Ellen Perry. Her work since then and several of her honours are sketched in the filmography below. Roberts was featured in a New York Times article on film editing in 2012. She has been selected for membership in the American Cinema Editors, which entitles editors to append "A.C.E." to their film credits.

Frances Reid (director)
Frances Reid is an American filmmaker, producer and cinematographer known for her documentaries. She has been in filmmaking for three decades. In 1994, she was nominated alongside director Dee Mosbacher for an Academy Award for Best Documentary Short for Straight from the Heart, which explored relationships between straight parents and their gay children. She was again nominated for an Oscar for producing and directing Long Night's Journey into Day (2000).
Jacobs Building (Buena Vista, Colorado)
The Jacobs Building, at 414 Main St. in Buena Vista, Colorado, was built in 1888.  It was listed on the National Register of Historic Places in 2011.  The listing included two contributing buildings and a contributing structure, with one apparently being a jailhouse.

It has served as a restaurant and hotel, and has been known as Johnson Building and as Mother's Bistro.

In 2019, the Historic Preservation Commission of Buena Vista was considering an application to list "the Jailhouse Building located at 412 E. Main Street as a local historic building subject to the requirements of Section 19 of the Town of Buena Vista Municipal Code."  The jailhouse building was covered in the National Register listing already; the local listing would strengthen local protection for the building.

Buena Vista, Colorado
Buena Vista (/ˈbjuːnə ˈvɪstə/ BEW-nə VISS-tə) is a statutory town located in Chaffee County, Colorado, United States. The town population was 2,855 at the 2020 United States census. From 1888 until 1928, Buena Vista served as the county seat of Chaffee County.
Coelomomyces elegans
Coelomomyces elegans is a species of mosquito parasitic fungi, in the genus Coelomomyces. It has been found in Culex gelidus mosquitoes, in Matara, Sri Lanka.

It is distinguishable from other species of Coelomomycetaceae by its resting sporangia, which are ornamented by circular depressed areas with papillae. Other distinct features include prominent vertical striae within ridges and a dehiscence split bordered by papillae.

Matara, Sri Lanka
Matara (Sinhala: මාතර, romanized: Māthara; Tamil: மாத்தறை) is a major city in Sri Lanka, on the southern coast of Southern Province. It is the second largest city in Southern Province. It is 160 km (99 mi) from Colombo. It is a major commercial hub, the administrative capital and largest city of Matara District.

Ethnic composition in Matara DS Division according to 2012 census data is Sinhalese 111,039 (95.88%), Muslims 4,296 (3.71%), Tamils 326 (0.28%), Others 144 (0.12%).
Paraboot
Paraboot is  a brand of shoes and boots made in France at a factory in Saint-Jean-de-Moirans, Isère. Paraboot began  in Izeaux in 1908 and remains a family business, currently in the fourth generation. Esquire magazine called its Michael derby ”perhaps the most reliably stylish shoe of all time.”

Exports make up 50% of sales. Paraboot is retailed by J. Crew, Nordstrom, Noah, Todd Snyder, Drake's 
, and independent menswear stores. The brand has collaborated with Engineered Garments, the North Face, KAPTAIN SUNSHINE, Aimé Leon Dore, and Drake’s.
It was created by Richard-Ponvert.

Engineered Garments
Engineered Garments is a clothing, footwear and accessories brand founded by Japanese-American Daiki Suzuki. It was founded in 1999.

The brand has collaborated with Uniqlo, Gola, Paraboot, K-Swiss, Hoka One One, Converse, Reebok, and others.
Certified (song)
"Certified" is a song by American rapper Glasses Malone, released as the first single from his third studio album, Beach Cruiser. The track is produced by DJ Toomp and features Senegalese-American artist Akon.

West coast artists such as Jay Rock, E-40, and Mack 10 make cameos in the music video. The music video premiered on BET's 106 & Park on March 4, 2008.

The remix features Bun B, Kam and Lil Wayne.

Another remix by artists signed to Malone's record label Blu Division featuring Conflict, Quiz, The Bloc Boyz, K-Style, Roc Slanga and Akon.

E-40
Earl Tywone Stevens (born November 15, 1967), better known by his stage name E-40, is an American rapper. Stevens is a founding member of the rap group The Click and the founder of Sick Wid It Records. He has released 27 studio albums to date, appeared on numerous movie soundtracks, and has also done guest appearances on a host of other rap albums. Initially an underground artist, his 1995 solo album In a Major Way opened him up to a wider audience. Beginning in 1998, he began collaborating with mainstream rappers outside the San Francisco Bay Area. He rose to higher mainstream popularity in 2006 with his single "Tell Me When to Go", which was produced by Lil Jon.
Lakeside Village, Oklahoma
Lakeside Village is a census-designated place (CDP) in Comanche County, Oklahoma, United States. It was first listed as a CDP prior to the 2020 census. As of the 2020 census, Lakeside Village had a population of 162.

The CDP is in northern Comanche County, on the west side of Lake Ellsworth, on the south side of its Chandler Creek inlet. It is bordered to the west by U.S. Routes 62/281 and is 14 miles (23 km) north of Lawton and 7 miles (11 km) south of Apache. Via U.S. Route 277, it is 7 miles west-northwest of Elgin.

Lake Ellsworth is an impoundment on East Cache Creek, a south-flowing tributary of the Red River.

U.S. Route 62
U.S. Route 62 or U.S. Highway 62 (US 62) is an east–west United States Highway in the southern and northeastern United States. It runs from the Mexican border at El Paso, Texas, to Niagara Falls, New York, near the Canadian border. It is the only east–west United States Numbered Highway that connects Mexico and Canada. Parts of US 62 follow what once was the Ozark Trail, including the historic bridge across the South Canadian River in Newcastle, Oklahoma (the first structure built with federal highway funds in Oklahoma after lobbying efforts by Stanley Draper). This bridge was damaged beyond repair by the 2013 Moore tornado that struck Newcastle and Moore, Oklahoma. The highway is signed north–south in New York and Pennsylvania, reflecting its directional orientation in both states, and is signed east-west for the remainder of its course.
Mona Barthel
Mona Barthel (born 11 July 1990) is a German tennis player.
On 18 March 2013, she reached her best singles ranking of world No. 23. On 14 September 2015, she peaked at No. 63 in the doubles rankings.

Barthel has won four singles and three doubles titles on the WTA Tour, one doubles title on the WTA Challenger Tour as well as five singles titles and one doubles title on the ITF Circuit in her career.

Sachia Vickery
Sachia Vickery (/ˈsɑːʃə/ SAH-shə; born May 11, 1995) is an American professional tennis player. She reached a career-high of No. 73 in the WTA rankings on July 30, 2018.
Vickery, a former USTA junior national champion, has also won three singles and three doubles titles on the ITF Circuit.

Her best results on the WTA Tour came at the 2018 Auckland Open and the 2018 Monterrey Open, where she reached the semifinals.
AsiaNews
AsiaNews is an official press agency of the Catholic Church's Pontifical Institute for Foreign Missions (PIME). The editor-in-chief of AsiaNews is Father Bernardo Cervellera, a PIME missionary who also heads Agenzia Fides, the official news agency of the Vatican. Prominent British Bangladeshi journalist and human rights activist William Gomes worked for Asia news.

Agenzia Fides
Agenzia Fides is the news agency of the Vatican. It is based in the Palazzo di Propaganda Fide in Rome. It is part of the Congregation for the Evangelization of Peoples. It was formed on 5 June 1927, as the first missionary news agency of the Roman Catholic Church and was approved by Pope Pius XI.
Lami al-Darari
Lami al-Darari ala Jami al-Bukhari (Urdu: لامع الدراري على جامع البخاري) is a multi-volume commentary on Sahih al-Bukhari, which is based on the teachings of Rashid Ahmad Gangohi. The original lessons were recorded in Arabic by Yahya Kandhlawi, a student of Gangohi, and later expanded upon by his son, Zakariyya Kandhlawi, with extensive footnotes at the insistence of Hussain Ahmad Madani. The commentary was completed in 1968. Its primary objective is to provide detailed explanations, discussions, and insights into the various sections, topics, and issues addressed in Sahih al-Bukhari. Additionally, it incorporates additional research, references to other scholarly works, and offers a defense of the Hanafi school of Islamic jurisprudence.

Yusuf Banuri
Sayyid Muhammad Yousuf Banuri (7 May 1908 – 17 October 1977) was a Pakistani Islamic scholar, who was the founder of Jamia Uloom-ul-Islamia and former President and Vice President of Wifaq-ul-Madaris al-Arabia, Pakistan from 30 May 1973 to 17 October 1977.

He also served as Emir of the Aalmi Majlis Tahaffuz Khatm-e-Nubuwwat from 1974 to 1977.
Ulrike Deppe
Ulrike Deppe (9 December 1953 in Lippstadt) is a former West German slalom canoeist who competed at the international level from 1969 to 1983.

She won three medals in the K1 event at the ICF Canoe Slalom World Championships with a gold (1981) and two silvers (1969, 1975). She also won two golds (1969, 1981) and two silvers (1971, 1979) in the K1 team event at the World Championships.

Deppe finished seventh in the K1 event at the 1972 Summer Olympics in Munich.

Lippstadt
Lippstadt (German pronunciation: [ˈlɪpʃtat] ⓘ) is a town in North Rhine-Westphalia, Germany. It is the largest town within the district of Soest. Lippstadt is situated about 60 kilometres east of Dortmund, 40 kilometres south of Bielefeld and 30 kilometres west of Paderborn.