About: Rng (algebra)

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In mathematics, and more specifically in abstract algebra, a rng (or non-unital ring or pseudo-ring) is an algebraic structure satisfying the same properties as a ring, but without assuming the existence of a multiplicative identity. The term rng (IPA: /rʊŋ/) is meant to suggest that it is a ring without i, that is, without the requirement for an identity element. A number of algebras of functions considered in analysis are not unital, for instance the algebra of functions decreasing to zero at infinity, especially those with compact support on some (non-compact) space.

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rdf:type	yago:Artifact100021939 yago:Object100002684 yago:PhysicalEntity100001930 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity building yago:Structure104341686 yago:Whole100003553 yago:WikicatAlgebraicStructures
rdfs:label	Pseudoanillo (es) Pseudo-anneau (fr) 유사환 (ko) 擬環 (ja) Rng (algebra) (en) 伪环 (zh)
rdfs:comment	En matemáticas entendemos por pseudoanillo una Estructura algebraica de la forma donde R es un conjunto, la base del pseudoanillo, + y * son operaciones binarias y existe 0, un elemento del conjunto, el cero del pseudoanillo, tal que es un Grupo abeliano es un semigrupo. Las operaciones + y * se dicen respectivamente suma y producto del pseudoanillo. Cuando el producto de un pseudoanillo posee una unidad, que notamos con 1, es decir, cuando es un monoide, es una estructura llamada anillo. Si el producto de un pseudoanillo es conmutativo, la estructura se llama . * Datos: Q17102802 (es) 환론에서 유사환(類似環, 영어: pseudoring 또는 영어: rng [rʌŋ])은 환과 유사하나, 곱셈에 대한 항등원을 갖지 않을 수 있는 구조다. (ko) 抽象代数学において必ずしも単位元を持たない環 (rng) あるいは擬環（ぎかん、英: pseudo-ring）、非単位的環（ひたんいてきかん、英: non-unital ring）は、乗法単位元の存在以外の環の公理をすべて満たすような代数的構造を言う。英語では少しおどけて、「単位元」（identity, これをしばしば 1 で表す）の無い「環」 (ring) だからということで、「rng」と呼称することもある。環の公理に乗法単位元の存在を含めない文献もあり、この文脈では本項に云う概念は単に「環」と呼称される。また、修飾辞「非単位的」は「必ずしも単位的でない」という意味で用いられるが、本項ではその意味では専ら「擬環」を（あるいは直接的に「必ずしも」を付けて）用い、単独の「単位的」・「非単位的」を単位元の有無を強調する意味でのみ用いる（つまり、非単位的であるといった場合には実際に単位元を持たない）。 (ja) 抽象代数，一个伪环（即无乘法单位环）是代数结构环的研究过程中，专指无乘法单位元素的环，“rng” 代表沒有乘法单位元素（英："multiplicative identity"）的環（ring）。 (zh) En mathématiques, un pseudo-anneau est une des structures algébriques utilisées en algèbre générale. C'est un ensemble muni d'une addition et d'une multiplication qui vérifient les mêmes axiomes que celles d'un anneau, à ceci près qu'on n'exige pas la présence d'un élément neutre pour la multiplication. Une minorité d'auteurs ne demandent pas aux anneaux d'avoir un neutre multiplicatif ; si l'on se réfère à leurs conventions, le présent article traite donc de ce qu'ils appellent des anneaux. (fr) In mathematics, and more specifically in abstract algebra, a rng (or non-unital ring or pseudo-ring) is an algebraic structure satisfying the same properties as a ring, but without assuming the existence of a multiplicative identity. The term rng (IPA: /rʊŋ/) is meant to suggest that it is a ring without i, that is, without the requirement for an identity element. A number of algebras of functions considered in analysis are not unital, for instance the algebra of functions decreasing to zero at infinity, especially those with compact support on some (non-compact) space. (en)
dcterms:subject	Algebras Ring theory Algebraic structures
Wikipage page ID	3405004 (xsd:integer)
Wikipage revision ID	1107469419 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Schwartz space Subcategory Algebraic structure Homomorphism Vector space Limit of a sequence Quotient ring Rng (algebra) Algebras Ring theory Compact space Compact support Continuous function Mathematical analysis Mathematics Matrix (mathematics) Generalized inverse Quinary Emmy Noether Multiplicative identity Nilpotent Linear operator Zero ring Functional analysis Ideal (ring theory) Subgroup Maximal ideal Algebraic structures Semigroup Cyclic group Even number Field (mathematics) Binary operations Rank (linear algebra) Ring (mathematics) Surjective Abelian group Abstract algebra Support (mathematics) Reflective subcategory Idempotence Idempotent element (ring theory) Integer Category theory Semiring Sequence Set (mathematics) Universal property Simple ring Injective Topological space Module (algebra) Ring homomorphism Universal construction Ring axioms Test function Submodule Functional composition Category of all rings Distributive law Inclusion functor Kernel (ring theory) Left adjoint Dimension (linear algebra) Theory of distributions
Link from a Wikipage to an external page	https://doi.org/10.1007/BF01464225
sameAs	Rng (algebra) Rng (algebra) Rng (algebra) Rng (algebra) Rng (algebra) Rng (algebra) Rng (algebra)

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