In mathematics, in semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed using a semigroup and an ideal of the semigroup. Let S be a semigroup and I be an ideal of S. Using S and I one can construct a new semigroup by collapsing I into a single element while the elements of S outside of I retain their identity. The new semigroup obtained in this way is called the Rees factor semigroup of S modulo I and is denoted by S/I.
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| - Rees factor semigroup (en)
- Kongruencje Reesa (pl)
- Semigrupo fator de Rees (pt)
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| - Kongruencje Reesa - rodzaj kongruencji w teorii półgrup. Nazwa pochodzi od nazwiska Davida Reesa. Kongruencje Reesa zadawane są przez ideały półgrupy, podobnie jak kongruencje w pierścieniach. Jednak nie wszystkie kongruencje w półgrupach są kongruencjami Reesa. (pl)
- In mathematics, in semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed using a semigroup and an ideal of the semigroup. Let S be a semigroup and I be an ideal of S. Using S and I one can construct a new semigroup by collapsing I into a single element while the elements of S outside of I retain their identity. The new semigroup obtained in this way is called the Rees factor semigroup of S modulo I and is denoted by S/I. (en)
- Em matemática, na teoria de semigrupos, um semigrupo fator de Rees (também chamado de semigrupo quociente de Rees ou apenas fator de Rees), assim chamado em referência a David Rees, é um certo tipo de semigrupo construído usando um semigrupo e um ideal do semigrupo. Seja S um semigrupo e seja I um ideal de S. Usando S e I, pode-se construir um novo semigrupo fundindo I em um único elemento, e mantendo a identidade dos elementos de S fora de I. O novo semigrupo obtido desta forma é chamado de semigrupo fator de Rees de S módulo I e é denotado por S/I. (pt)
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| - In mathematics, in semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed using a semigroup and an ideal of the semigroup. Let S be a semigroup and I be an ideal of S. Using S and I one can construct a new semigroup by collapsing I into a single element while the elements of S outside of I retain their identity. The new semigroup obtained in this way is called the Rees factor semigroup of S modulo I and is denoted by S/I. The concept of Rees factor semigroup was introduced by David Rees in 1940. (en)
- Em matemática, na teoria de semigrupos, um semigrupo fator de Rees (também chamado de semigrupo quociente de Rees ou apenas fator de Rees), assim chamado em referência a David Rees, é um certo tipo de semigrupo construído usando um semigrupo e um ideal do semigrupo. Seja S um semigrupo e seja I um ideal de S. Usando S e I, pode-se construir um novo semigrupo fundindo I em um único elemento, e mantendo a identidade dos elementos de S fora de I. O novo semigrupo obtido desta forma é chamado de semigrupo fator de Rees de S módulo I e é denotado por S/I. O conceito de semigrupo fator de Rees foi introduzido por David Rees em 1940. (pt)
- Kongruencje Reesa - rodzaj kongruencji w teorii półgrup. Nazwa pochodzi od nazwiska Davida Reesa. Kongruencje Reesa zadawane są przez ideały półgrupy, podobnie jak kongruencje w pierścieniach. Jednak nie wszystkie kongruencje w półgrupach są kongruencjami Reesa. (pl)
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