OpenLLM-France/wikimedia huggingface dataset:
# Prime element

In mathematics, specifically in abstract algebra, a prime element of a commutative ring is an object satisfying certain properties similar to the prime numbers in the integers and to irreducible polynomials. Care should be taken to distinguish prime elements from irreducible elements, a concept that is the same in UFDs but not the same in general.

## Definition

An element p of a commutative ring R is said to be prime if it is not the zero element or a unit and whenever p divides ab for some a and b in R, then p divides a or p divides b. With this definition, Euclid's lemma is the assertion that prime numbers are prime elements in the ring of integers. Equivalently, an element p is prime if, and only if, the principal ideal (p) generated by p is a nonzero prime ideal. (Note that in an integral domain, the ideal (0) is a prime ideal, but 0 is an exception in the definition of 'prime element'.)
Interest in prime elements comes from the fundamental theorem of arithmetic, which asserts that each nonzero integer can be written in essentially only one way as 1 or −1 multiplied by a product of positive prime numbers. This led to the study of unique factorization domains, which generalize what was just illustrated in the integers.
Being prime is relative to which ring an element is considered to be in; for example, 2 is a prime element in Z but it is not in Z[i], the ring of Gaussian integers, since 2 = (1 + i)(1 − i) and 2 does not divide any factor on the right.

## Connection with prime ideals

An ideal I in the ring R (with unity) is prime if the factor ring R/I is an integral domain. Equivalently, I is prime if whenever $ab\in I$ then either $a\in I$ or $b\in I$.
In an integral domain, a nonzero principal ideal is prime if and only if it is generated by a prime element.

## Irreducible elements

Prime elements should not be confused with irreducible elements. In an integral domain, every prime is irreducible but the converse is not true in general. However, in unique factorization domains, or more generally in GCD domains, primes and irreducibles are the same.

## Examples

The following are examples of prime elements in rings:
* The integers ±2, ±3, ±5, ±7, ±11, ... in the ring of integers Z
* the complex numbers (1 + i), 19, and (2 + 3i) in the ring of Gaussian integers Z[i]
* the polynomials x$^2$ − 2 and x$^2$ + 1 in Z[x], the ring of polynomials over Z.
* 2 in the quotient ring Z/6Z
* x$^2$ + (x$^2$ + x) is prime but not irreducible in the ring Q[x]/(x$^2$ + x)
* In the ring Z$^2$ of pairs of integers, (1, 0) is prime but not irreducible (one has (1, 0)$^2$ = (1, 0)).
* In the ring of algebraic integers $\mathbf {Z} [{\sqrt {-5}}],$ the element 3 is irreducible but not prime (as 3 divides $9=(2+{\sqrt {-5}})(2-{\sqrt {-5}})$ and 3 does not divide any factor on the right).
# Network loudspeaker

A conventional loudspeaker is an electromechanical transducer that converts an electrical signal into sound. If locally powered, this can also be termed an active loudspeaker, meaning it contains an audio power amplifier that drives the loudspeaker. A network loudspeaker implies the ability to send audio to such a device from a network connection, usually over an Ethernet network or the Internet. In many cases this type of speaker also contains digital signal processing (DSP) to provide the audio crossover and other tonal functions that exist in conventional speakers. Network speakers are also known as IP speakers. In many cases the IP speaker is created from an IP audio endpoint — a device with the requisite network connection and ability to process audio packets, but without the actual physical speaker portion — that provides amplified audio to a conventional loudspeaker or unamplified audio (i.e. line-out) to an amplified speaker or system.

## History

Network audio was first introduced in 1983 by John Detreville and W. David Sincoskie of Bell Labs in the IEEE paper "A Distributed Experimental Communications System". Subsequently, in 1988, Polle T. Zellweger, Douglas B. Terry and Daniel C. Swinehart of Xerox PARC introduced audio over Ethernet at the 2nd IEEE Conference in a paper entitled "An Overview of the Etherphone System and its Applications". The very closely related technology (nearly synonymous), Voice over IP (VoIP), which generally consists at a minimum of a microphone on one end, a speaker on the other end, with a network connecting them; began widespread use in 1998 with PCs, followed shortly after by dedicated hardware (phones with built-in VoIP capabilities). Subsequently, the first Squeezebox, using networked audio, was released in 2001 and Philips released its IP audio device also in 2001, the FW-i1000. Countless IP audio devices have since proliferated into most major audio markets.

## Designs

The audio content played by the processor in an IP speaker is communicated from its source across a packet-switched data network using IPv4 and IPv6 addressing with a User Datagram Protocol (UDP) or Real-time Transport Protocol (RTP). The IP Speaker connects to Unicast or Multicast addresses to enable the delivery of streamed data from a source on the network, to arrive at a single speaker or many speakers respectively.
# The Wife Between Us

The Wife Between Us is a 2018 thriller novel written by Greer Hendricks and Sarah Pekkanen.

## Plot

Vanessa is watching her ex husband's new fiancée. She lives with her aunt in New York City and is working at a clothing store to get by after her divorce from Richard. Nellie is Richard's new fiancée, a pre-school teacher. We learn that Vanessa and Nellie are the same person (Vanessa being her present self, and Nellie being her past self). It was Richard's idea to give Vanessa the nickname Nellie, because when they first met, she was a "nervous nellie."
Part two starts with what happened between Vanessa and Richard. Richard started gas-lighting and abusing Vanessa, cutting her off from friends and family. It becomes worse after they are unable to have children, which both believe is due to an abortion she had in college which she did not tell him about, partially due to the father being one of her professors, who was married. She starts seeing a therapist, who points out that Vanessa needs to leave. However, Vanessa knows Richard will not let her go and that he needs to decide to divorce her himself. She sets Richard up with his assistant, Emma, and the two begin an affair. Vanessa is finally free of her abusive marriage only to find out that Richard intends to marry Emma. To save her, Vanessa tells Emma Richard's reality but Emma does not believe her. Emma tells Richard, who confronts Vanessa. Vanessa tells Emma the first signs she saw of him controlling her. Emma then realizes she is being manipulated by Richard and agrees to leave him.
Vanessa visits Richard and threatens to reveal everything, provoking Richard into strangling her before Emma and Richard's sister, Maureen, intervene. Flash-forward, Richard is in a psych ward. Vanessa visits him only to find Maureen there; she seems to think there is something going on between the two. Vanessa tells her therapist she can finally move on. It is revealed that Vanessa's therapist is Richard's other ex wife, who he threw down a flight of stairs. It is also revealed that Emma is the daughter of the professor Vanessa had an affair with, and her parents' marriage ended after her mother found out. All three women are connected by their experiences.

## Critical reception

The New York Times wrote "The novel is halfway over before the first reveal, but it’s worth the wait, if only for its singularity. Then the twists come fast and furious."

## Film adaptation

In 2017 the film rights for The Wife Between Us were purchased by Steven Spielberg's Amblin Partners.
# Dallas Thomas

Dallas Treymell Thomas (born October 30, 1989) is an American former professional football player who was a guard in the National Football League (NFL). He was selected by the Miami Dolphins in the third round of the 2013 NFL draft. He played college football for the Tennessee Volunteers.

## Early life

Thomas was born in Baton Rouge, Louisiana. While attending Scotlandville Magnet High School in Baton Rouge, he played high school football for the Scotlandville Hornets.

## College career

Thomas attended the University of Tennessee, where he played for the Tennessee Volunteers football team from 2008 to 2012. During his college career, he started 37 of 50 games in which he appeared at offensive tackle and guard. As a senior in 2012, he received third-team All-American honors from CBSSports.com, and was a second-team All-Southeastern Conference (SEC) selection.

## Professional career
### Miami Dolphins

The Miami Dolphins selected Thomas in the third round (77th overall) of the 2013 NFL draft.
On October 9, 2016, Thomas started at left guard after Billy Turner was moved to left tackle since both the starting left tackle, Branden Albert, and the backup left tackle, Laremy Tunsil, both missed the game due to illness and injury, respectively. Thomas and Turner were both released two days later after they had a disastrous performance during the 30–17 loss to the Tennessee Titans.

### Philadelphia Eagles

On January 18, 2017, Thomas signed a reserve/future contract with the Eagles. He was waived on September 2, 2017.

### Memphis Express

In 2018, Thomas signed with the Memphis Express of the AAF for the 2019 season. The league ceased operations in April 2019.

### St. Louis Battlehawks

In October 2019, Thomas was selected by the St. Louis BattleHawks as their 19th pick in the third round of the Offensive Line phase of the 2020 XFL Draft. On April 10, 2020, the XFL league suspended operations, thus cancelling Thomas' contract.
# Sam Reid (footballer, born 1872)

Samuel Alexander Reid (born 17 June 1872) was an Australian rules footballer who played with Carlton in the Victorian Football League (VFL).
# Des Meadowcroft

Des Meadowcroft (31 March 1880 – 22 September 1959) was an Australian rules footballer who played with Carlton in the Victorian Football League (VFL).
# Alf Moore

Arthur Edward "Alf" Moore (21 March 1870 – 15 July 1950) was an Australian rules footballer who played for the Carlton Football Club in the Victorian Football League (VFL).

## Family

The son of William Trivess Moore (1844-1896), and Frances Emily Moore (1852–1880), née Cowan, Arthur Edward Moore was born at Richmond, Victoria on 21 March 1870.
He married Letitia Tyley (1875-1962) in 1899.
His cousin, Robert Clements "Bob" Moore (1872–1938) was also a VFL footballer; he played 2 games with the Melbourne Football Club in 1898.

## Football

Recruited from Norwood, he played 2 games for Carlton.

## Death

He died at Hawthorn, Victoria on 15 July 1950.
# Thrust Air 2000

A Thrust Air 2000 (commonly known as a thrust air coaster) is a unique form of launched roller coaster created by S&S Worldwide, Inc., that uses refrigerated, compressed air to shoot a rubber-wheeled car down a steel track. Do-Dodonpa, located at Fuji-Q Highland, was the only production model in existence until it permanently closed in March 2024. It was built by S&S Worldwide of Logan, Utah. It was once the fastest roller coaster in the world and still holds the record of the world's fastest acceleration on a roller coaster. Another model, the Hypersonic XLC, was opened at Kings Dominion in 2001, but it was later closed and put up for sale in 2007. Both models were fabricated by Intermountain Lift, Inc.

## Prototype

The prototype Thrust Air 2000 was made in 1999 at the S&S Power plant in Utah. That prototype was bought by Paramount directly from the plant and then built at Kings Dominion.

### Stats

* Height: 165 ft (50 m).
* Climb: 90 degrees
* Drop: 90 degrees
* Acceleration: 0-80 mph (0-128.7 km/h) in 1.8 sec
* Top Speed: about 80 mph (130 km/h)
* Launch System: Ingersoll-Rand screw type compressor
* Track layout: Out-and-back roller coaster
* Track type: I-beam
# Jim Opie

Archelaus James Opie (1 March 1883 – 20 July 1981) was an Australian rules footballer who played with St Kilda and Carlton in the Victorian Football League (VFL).
# Gordon Ross (Australian footballer)

Thomas Gordon Ross (26 July 1878 – 23 August 1952) was an Australian rules footballer who played with Fitzroy and Carlton.

## Sources

* ↑ "Family Notices". The Sydney Morning Herald. National Library of Australia. 26 August 1952. p. 16. Retrieved 21 September 2014.
* ↑ "Gordon Ross". Blueseum – Online Carlton Football Club Museum. Retrieved 31 August 2014.
* Holmesby, Russell & Main, Jim (2009). The Encyclopedia of AFL Footballers. 8th ed. Melbourne: Bas Publishing.
* Gordon Ross's playing statistics from AFL Tables
* This Australian rules football biography of a person born in the 1870s is a stub. You can help Wikipedia by expanding it.
* v
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# Multistrada Arah Sarana

PT Multistrada Arah Sarana Tbk is an Indonesian tire manufacturer. They sell tires under the brands Achilles and Corsa. It is considered to be one of the largest tire manufacturers in Indonesia, operating factories of 55 hectares (140 acres) and 128 hectares (320 acres), located in East Cikarang, Indonesia. Since 2019, it is a publicly-traded subsidiary of French manufacturer Michelin.

## Products

MASA manufactures tires for passengers cars, commercial cars, trucks, buses, and competition vehicles, as well as performance and industrial tires which are used in the international market. Multistrada Arah Sarana also manufactures tires under the brand name Achilles and Corsa, as well as Michelin, BFGoodrich and Uniroyal.

## History

PT Multistrada Arah Sarana Tbk or MASA, was known as PT Oroban Perkasa when it first started in 1988. They had built motorcycle tires and cars, with their own brands, which are Strada, Achilles, and Corsa. MASA received assistance from Pirelli (Italy) and Continental (Germany) to improve their manufacturing technology. During the 1997 Asian financial crisis, the company was given to Badan Penyehatan Perbankan Nasional (BPPN) to save the company. In 2004, the company then was taken under the guidance of PT Indokemika Jayatama. They made the company available for IPO in 2005. Through equity and syndicated loans, the company has been able to expand their capital and increase productivity and quality.
Since then, Achilles Radial has expanded its product line into the industrial market. They started to build tires for trucks and buses with their Solid Tire or known as ST and TBR for their bus tires. The company also improved its internal quality by taking a more aggressive stance towards consumer safety. They gained their certificates for the ISP/TS 16949:2009 and ISO/IEC 17025:2008 for Quality Management System and a couple of other product certificates such as SNI, CCC, Inmetro, BIS, ECE-30, ECE-54, GSO, DOT, FMVSS 139.
On 22 January 2019, it was announced that MASA was acquired by French-based manufacturer Michelin. On 19 June that year, Michelin owns 99.64% of the share capital of Multistrada.
# Charlie Oliver (Australian footballer)

Charles Joseph Oliver (9 September 1874 – 29 December 1917) was an Australian rules footballer who played with Carlton in the Victorian Football League (VFL). A medical practitioner, he enlisted in the First AIF, and died while in service.

## Family

The son of Robert Oliver and Emily Ann Oliver, née Parkinson, Charles Joseph Oliver was born at Sofala, near Bathurst, in New South Wales, on 9 September 1874.
He married Ellen Frances Mahony (1870–1917) in 1905. They had two children, Norman Joseph Oliver (1906–), and Charles Patrick Oliver (1909–1956).

## Education

He commenced his medical studies at the University of Melbourne in 1892.

## Football
### Carlton Imperials

Oliver played his early football at Carlton Imperials.

### Carlton (VFL)

He played just one VFL game for Carlton, against Melbourne at the MCG, on 7 July 1900 (round 10).
Selected at centre half-forward to play against Melbourne's exceptional centre half-back Jack Purse, and replacing Carlton's regular centre half-forward Bill McNamara (in the one game that McNamara did not play for the 1900 season), Oliver kicked one goal in a soundly beaten team: Melbourne 9.14 (68) to Carlton's 5.3 (33).

## Medical Practitioner

He was a qualified medical practitioner, having been awarded his Medicinae Baccalaureus et Baccalaureus Chirurgiae (M.B. et Ch.B.) from Melbourne University, in absentia, in March 1903, and having been entered into the Victorian medical register on 2 October 1903.
In 1905/1907 he was serving as the health officer for the Shire of Kerang at Quambatook in northern Victoria; and in the Shire of Berwick in 1912. At the time of his enlistment he was practising in Jeparit in Western Victoria.

## Military service

He served with the Australian Army Medical Corps in World War I.

## Death

Oliver was on his way back to the army camp in Seymour on 27 December 1917 when he was thrown off a shying horse.
He had never ridden the horse before; and, distressed by having to wait far too long for motor transport, he had borrowed the strange horse in his eagerness to return to camp. It seems that some of the difficulty he had controlling the shying horse may have been due to not adjusting the length of the saddle's stirrups to suit his leg length: see the full account provided by the investigation into his death at pp. 44–51 of his Service record.
He died of a cerebral haemorrhage two days later at the Base Military Hospital in Melbourne (just 12 weeks after his wife's death).
He was given a military funeral, and was buried at the Williamstown General Cemetery. Although he clearly died whilst serving in the First AIF, and although he received a military funeral, (for some unexplained reason) he is not listed on the Australian War Memorial's Roll of Honour.
# Ikot Ibiok

Ikot Ibiok is a village in Eket local government area of Akwa Ibom State.
# Maurie Collins

Maurice Ignatius Collins (21 July 1876 – 8 November 1943) was an Australian rules footballer who played for Essendon in the Victorian Football League (VFL).

## Family

The son of Timothy Collins (1843-1899), and Catherine Collins (1846-1928), née Nunan, Maurice Ignatius Collins was born at Clifton Hill, Victoria on 21 July 1876.
He married Eileen Mary Marsh (1886-1968) in 1906. They had four children; one of whom, Alan Collins (1914-1914) died in his infancy. In 1927, another of their three sons, Maurice Xavier Collins (1907-1955), was captain of the Old Xaverians Football Club in the Metropolitan Amateur Football Association (MAFA).

## Football
### Essendon (VFL)

Collins played his early football with the Albert Park Football Club. He was injured during the 1897 VFL finals series but according to some sources made one appearance. Collins, a defender, was a member of Essendon's 1901 premiership team, as a back pocket. A VFL representative, he was the vice captain of Essendon for his final season.

### 1899 team of "champions"

At the end of the 1899 season, in the process of naming his own "champion player", the football correspondent for The Argus, Reginald Wilmot ("Old Boy"), selected a team of the best players of the 1899 VFL competition:
* Backs: Maurie Collins (Essendon), Bill Proudfoot (Collingwood), Peter Burns (Geelong).
* Halfbacks: Pat Hickey (Fitzroy), George Davidson (South Melbourne), Alf Wood (Melbourne).
* Centres: Fred Leach (Collingwood), Firth McCallum (Geelong), Harry Wright (Essendon).
* Wings: Charlie Pannam (Collingwood), Eddie Drohan (Fitzroy), Herb Howson (South Melbourne).
* Forwards: Bill Jackson (Essendon), Eddy James (Geelong), Charlie Colgan (South Melbourne).
* Ruck: Mick Pleass (South Melbourne), Frank Hailwood (Collingwood), Joe McShane (Geelong).
* Rovers: Dick Condon (Collingwood), Bill McSpeerin (Fitzroy), Teddy Rankin (Geelong).
From those he considered to be the three best players — that is, Condon, Hickey, and Pleass — Wilmot selected Pat Hickey as his "champion player" of the season.

## Death

He died at Kew, Victoria on 8 November 1943.
# Jack O'Loughlin (Australian footballer)

John Joseph O'Loughlin (10 August 1873 – 8 August 1960) was an Australian rules footballer who played for Geelong and St Kilda and an umpire in the Victorian Football League (VFL).
O'Loughlin started his career at Footscray, while they were a Victorian Football Association (VFA) club, but got his chance in the big league when he crossed to Geelong in 1898. O'Loughlin spent 1898 and 1901 at Geelong for 22 matches and 1902 at St Kilda for three matches.
When boundary umpires were introduced to the VFL in 1904, O'Loughlin was one of the first appointed. He officiated in 91 matches until 1910, including the 1909 Grand Final, and also field umpired in country Victoria.
# Bert Sharpe

Albert 'Bert' Sharpe (6 May 1878 – 10 January 1918) was an Australian rules footballer who played for the Fitzroy Football Club and South Melbourne Football Club in the Victorian Football League (VFL).
Sharpe was a key position forward but could also play as a defender when required. He played at centre half-forward in the 1898 Fitzroy premiership side and went on to play 99 games for the club; some sources credit him as having played in Fitzroy's 1899 premiership team, thus making 100 Fitzroy appearances, but he was a late withdrawal from the side due to the death of his father the day before the Grand Final; his teammates wore black armbands for that match. He still brought up the 100 game milestone as he continued his career at South Melbourne in 1904.
He died young in 1918.
# Tommy O'Day

Thomas O'Day (8 October 1873 – 2 September 1905) was an Australian rules footballer who played for North Melbourne in the Victorian Football Association (VFA). He then played for the Imperials (a forerunner of East Fremantle) in the West Australian Football Association (WAFA), and then for Carlton in the Victorian Football League (VFL).

## Football

O'Day made his debut for the Carlton Football Club in Round 1 of the 1898 season. He was only with Carlton for the single season, playing 13 games and kicking 8 goals. The 8 goals he kicked made him the club's leading goal-kicker for that year -- the lowest leading goal tally in the club's history.
# EMAS

EMAS or Emas may refer to:

## Places

* Emas National Park, Brazil
* Emas, Paraíba, Brazil

## Other uses

* E.M.A.S., 2003 Malaysian-language album by Siti Nurhaliza
* EMAS (company), an oil and gas industry equipment company
* Emas (Malaysian TV channel)
* Emas bond, a Malaysian financial instrument
* Caloptilia emas, a moth of the family Gracillariidae
* East Midlands Ambulance Service, in England
* Eco-Management and Audit Scheme, an environmental management system
* Edinburgh Multiple Access System, a computer operating system
* EMAS Canada, a medical charity
* Engineered materials arrestor system, designed to mitigate runway excursions
* European Menopause and Andropause Society, a European medical association
* Expressway Monitoring and Advisory System, in Singapore
* MTV Europe Music Awards, a music awards show
* Proton EMAS, a range of concept cars