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Semianillo Halbring (algebraische Struktur) 반환 (수학) Semiring Напівкільце Полукольцо 半环 Halfring Demi-anneau Półpierścień Polookruh Semianello Semigelanggang 半環
rdfs:comment
Un semianello è una struttura algebrica formata da un insieme munito di due operazioni binarie, dette somma e prodotto e denotate rispettivamente con e , le quali verifichino le seguenti proprietà: 1. * Somma e prodotto sono operazioni associative: si ha cioè e per ogni terna di elementi di ; 2. * Esiste un (unico) elemento neutro per la somma, indicato con . Ciò significa che comunque si scelga in , vale ; 3. * Il prodotto è distributivo rispetto alla somma, vale a dire e per ogni scelta di , e in . 4. * Per ogni in , . Полукольцо — общеалгебраическая структура, похожая на кольцо, но без требования существования противоположного по сложению элемента. 在抽象代数中,半环是类似于环但没有加法逆元的代数结构。偶尔使用术语 rig - 这起源于一个笑话,rig 是没有 negative 元素的 ring。 추상대수학에서 반환(半環, 영어: semiring, rig)은 환과 유사하지만 덧셈의 역원이 존재하지 않는 대수 구조이다. 즉, 덧셈에 대하여 가환 모노이드를, 곱셈에 대하여 모노이드를 이루며, 분배 법칙이 성립하는 대수 구조이다. En álgebra, un semianillo​ ​ es una estructura algebraica más general que un anillo. Dalam aljabar abstrak, semigelanggang adalah struktur aljabar dengan gelanggang tanpa persyaratan setiap elemen menggunakan aditif invers. adalah bidang penelitian aktif, yang menghubungkan dengan struktur . Ein Halbring ist in der Mathematik die Verallgemeinerung der algebraischen Struktur eines Ringes, in der die Addition nicht mehr eine kommutative Gruppe, sondern nur noch eine kommutative Halbgruppe sein muss. Halbringe werden ebenso mit nicht kommutativer Addition sowie mit (absorbierender) und/oder definiert, die Definitionen in der Literatur sind nicht einheitlich. В абстрактній алгебрі напівкільце — алгебрична структура, схожа на кільце, але без вимоги існування оберненого елемента щодо операції додавання. Een halfring of ook semiring is een ring, maar zonder de eis dat elk element een tegengestelde moet hebben voor de optelbewerking. Een halfring is dus een verzameling R, waarop twee bewerkingen, een optelbewerking + en een vermenigvuldigingsbewerking x gedefinieerd zijn, die aan een aantal eisen voldoen.Elke ring is dus ook een halfring. Een voorbeeld van een halfring is de verzameling N van de natuurlijke getallen met de gewone optelling + en vermenigvuldiging x. De betekenis van de halfring is, dat er stellingen over bewezen kunnen worden, die dan voor alle halfringen gelden. In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. The term rig is also used occasionally—this originated as a joke, suggesting that rigs are rings without negative elements, similar to using rng to mean a ring without a multiplicative identity. Tropical semirings are an active area of research, linking algebraic varieties with piecewise linear structures. En mathématiques, un demi-anneau, ou semi-anneau, est une structure algébrique qui a les propriétés suivantes : * constitue un monoïde commutatif ; * forme un monoïde ; * est distributif par rapport à + ; * 0 est absorbant pour le produit, autrement dit: pour tout . Ces propriétés sont proches de celles d'un anneau, la différence étant qu'il n'y a pas nécessairement d'inverses pour l’addition dans un demi-anneau. Contrairement à ce qui se passe pour les anneaux, on ne peut démontrer que 0 est un élément absorbant à partir des autres axiomes. 抽象代数学において、半環(はんかん、英: semi-ring)とは環に類似した代数的構造で、環の公理から加法的逆元の存在を除いたようなもののことである。負元 (negative) の無い環 (ring) ということから rig という用語もしばしば用いられる。 Półpierścień – struktura algebraiczna podobna do pierścienia, która jednak nie musi być grupą względem dodawania. Oznacza to, że elementy półpierścienia nie muszą mieć elementu przeciwnego do siebie. Polookruh je v abstraktní algebře označení pro algebraickou strukturu podobnou okruhu, ve které ovšem nemusí pro všechny prvky existovat opačný prvek vzhledem ke sčítání. Jedná se o strukturu s dvěma binárními operacemi, která je vzhledem ke sčítání komutativním monoidem, vzhledem k násobení monoidem, pro operace platí distributivita a násobením nulovým prvkem vzniká nula. Komutativním polookruhem se rozumí polookruh, kde platí komutativita pro násobení.
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dbo:abstract
In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. The term rig is also used occasionally—this originated as a joke, suggesting that rigs are rings without negative elements, similar to using rng to mean a ring without a multiplicative identity. Tropical semirings are an active area of research, linking algebraic varieties with piecewise linear structures. En álgebra, un semianillo​ ​ es una estructura algebraica más general que un anillo. Un semianello è una struttura algebrica formata da un insieme munito di due operazioni binarie, dette somma e prodotto e denotate rispettivamente con e , le quali verifichino le seguenti proprietà: 1. * Somma e prodotto sono operazioni associative: si ha cioè e per ogni terna di elementi di ; 2. * Esiste un (unico) elemento neutro per la somma, indicato con . Ciò significa che comunque si scelga in , vale ; 3. * Il prodotto è distributivo rispetto alla somma, vale a dire e per ogni scelta di , e in . 4. * Per ogni in , . Si noti che la prima proprietà dice esattamente che e sono semigruppi, mentre la seconda proprietà specifica più completamente che è anche un monoide. 在抽象代数中,半环是类似于环但没有加法逆元的代数结构。偶尔使用术语 rig - 这起源于一个笑话,rig 是没有 negative 元素的 ring。 En mathématiques, un demi-anneau, ou semi-anneau, est une structure algébrique qui a les propriétés suivantes : * constitue un monoïde commutatif ; * forme un monoïde ; * est distributif par rapport à + ; * 0 est absorbant pour le produit, autrement dit: pour tout . Ces propriétés sont proches de celles d'un anneau, la différence étant qu'il n'y a pas nécessairement d'inverses pour l’addition dans un demi-anneau. Un demi-anneau est commutatif quand son produit est commutatif ; il est idempotent quand son addition est idempotente. Parfois on distingue les demi-anneaux et les demi-anneaux unifères : dans ce cas, la structure multiplicative n'est qu'un demi-groupe, donc ne possède pas nécessairement un élément neutre. En général, on demande aussi que . Un demi-anneau qui ne possède pas nécessairement un élément neutre pour sa multiplication est parfois appelé hémi-anneau (hemiring en anglais). Contrairement à ce qui se passe pour les anneaux, on ne peut démontrer que 0 est un élément absorbant à partir des autres axiomes. Een halfring of ook semiring is een ring, maar zonder de eis dat elk element een tegengestelde moet hebben voor de optelbewerking. Een halfring is dus een verzameling R, waarop twee bewerkingen, een optelbewerking + en een vermenigvuldigingsbewerking x gedefinieerd zijn, die aan een aantal eisen voldoen.Elke ring is dus ook een halfring. Een voorbeeld van een halfring is de verzameling N van de natuurlijke getallen met de gewone optelling + en vermenigvuldiging x. De betekenis van de halfring is, dat er stellingen over bewezen kunnen worden, die dan voor alle halfringen gelden. Ein Halbring ist in der Mathematik die Verallgemeinerung der algebraischen Struktur eines Ringes, in der die Addition nicht mehr eine kommutative Gruppe, sondern nur noch eine kommutative Halbgruppe sein muss. Halbringe werden ebenso mit nicht kommutativer Addition sowie mit (absorbierender) und/oder definiert, die Definitionen in der Literatur sind nicht einheitlich. Dalam aljabar abstrak, semigelanggang adalah struktur aljabar dengan gelanggang tanpa persyaratan setiap elemen menggunakan aditif invers. adalah bidang penelitian aktif, yang menghubungkan dengan struktur . 抽象代数学において、半環(はんかん、英: semi-ring)とは環に類似した代数的構造で、環の公理から加法的逆元の存在を除いたようなもののことである。負元 (negative) の無い環 (ring) ということから rig という用語もしばしば用いられる。 В абстрактній алгебрі напівкільце — алгебрична структура, схожа на кільце, але без вимоги існування оберненого елемента щодо операції додавання. Półpierścień – struktura algebraiczna podobna do pierścienia, która jednak nie musi być grupą względem dodawania. Oznacza to, że elementy półpierścienia nie muszą mieć elementu przeciwnego do siebie. 추상대수학에서 반환(半環, 영어: semiring, rig)은 환과 유사하지만 덧셈의 역원이 존재하지 않는 대수 구조이다. 즉, 덧셈에 대하여 가환 모노이드를, 곱셈에 대하여 모노이드를 이루며, 분배 법칙이 성립하는 대수 구조이다. Polookruh je v abstraktní algebře označení pro algebraickou strukturu podobnou okruhu, ve které ovšem nemusí pro všechny prvky existovat opačný prvek vzhledem ke sčítání. Jedná se o strukturu s dvěma binárními operacemi, která je vzhledem ke sčítání komutativním monoidem, vzhledem k násobení monoidem, pro operace platí distributivita a násobením nulovým prvkem vzniká nula. Komutativním polookruhem se rozumí polookruh, kde platí komutativita pro násobení. Definice polookruhu jako takového není zcela ustálená a za polookruh se někdy považuje i algebraická struktura, ve které není neutrální prvek vůči násobení ani vůči sčítání, tedy struktura se sčítáním a násobením, která je vzhledem ke sčítání , vzhledem k násobení pologrupou a pro operace platí distributivita. Полукольцо — общеалгебраическая структура, похожая на кольцо, но без требования существования противоположного по сложению элемента.
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