. . . "\uD658\uB860\uC5D0\uC11C \uC720\uC0AC\uD658(\u985E\u4F3C\u74B0, \uC601\uC5B4: pseudoring \uB610\uB294 \uC601\uC5B4: rng [r\u028C\u014B])\uC740 \uD658\uACFC \uC720\uC0AC\uD558\uB098, \uACF1\uC148\uC5D0 \uB300\uD55C \uD56D\uB4F1\uC6D0\uC744 \uAC16\uC9C0 \uC54A\uC744 \uC218 \uC788\uB294 \uAD6C\uC870\uB2E4."@ko . . . . . . . . "\u62BD\u8C61\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u5FC5\u305A\u3057\u3082\u5358\u4F4D\u5143\u3092\u6301\u305F\u306A\u3044\u74B0 (rng) \u3042\u308B\u3044\u306F\u64EC\u74B0\uFF08\u304E\u304B\u3093\u3001\u82F1: pseudo-ring\uFF09\u3001\u975E\u5358\u4F4D\u7684\u74B0\uFF08\u3072\u305F\u3093\u3044\u3066\u304D\u304B\u3093\u3001\u82F1: non-unital ring\uFF09\u306F\u3001\u4E57\u6CD5\u5358\u4F4D\u5143\u306E\u5B58\u5728\u4EE5\u5916\u306E\u74B0\u306E\u516C\u7406\u3092\u3059\u3079\u3066\u6E80\u305F\u3059\u3088\u3046\u306A\u4EE3\u6570\u7684\u69CB\u9020\u3092\u8A00\u3046\u3002\u82F1\u8A9E\u3067\u306F\u5C11\u3057\u304A\u3069\u3051\u3066\u3001\u300C\u5358\u4F4D\u5143\u300D\uFF08identity, \u3053\u308C\u3092\u3057\u3070\u3057\u3070 1 \u3067\u8868\u3059\uFF09\u306E\u7121\u3044\u300C\u74B0\u300D (ring) \u3060\u304B\u3089\u3068\u3044\u3046\u3053\u3068\u3067\u3001\u300Crng\u300D\u3068\u547C\u79F0\u3059\u308B\u3053\u3068\u3082\u3042\u308B\u3002 \u74B0\u306E\u516C\u7406\u306B\u4E57\u6CD5\u5358\u4F4D\u5143\u306E\u5B58\u5728\u3092\u542B\u3081\u306A\u3044\u6587\u732E\u3082\u3042\u308A\u3001\u3053\u306E\u6587\u8108\u3067\u306F\u672C\u9805\u306B\u4E91\u3046\u6982\u5FF5\u306F\u5358\u306B\u300C\u74B0\u300D\u3068\u547C\u79F0\u3055\u308C\u308B\u3002\u307E\u305F\u3001\u4FEE\u98FE\u8F9E\u300C\u975E\u5358\u4F4D\u7684\u300D\u306F\u300C\u5FC5\u305A\u3057\u3082\u5358\u4F4D\u7684\u3067\u306A\u3044\u300D\u3068\u3044\u3046\u610F\u5473\u3067\u7528\u3044\u3089\u308C\u308B\u304C\u3001\u672C\u9805\u3067\u306F\u305D\u306E\u610F\u5473\u3067\u306F\u5C02\u3089\u300C\u64EC\u74B0\u300D\u3092\uFF08\u3042\u308B\u3044\u306F\u76F4\u63A5\u7684\u306B\u300C\u5FC5\u305A\u3057\u3082\u300D\u3092\u4ED8\u3051\u3066\uFF09\u7528\u3044\u3001\u5358\u72EC\u306E\u300C\u5358\u4F4D\u7684\u300D\u30FB\u300C\u975E\u5358\u4F4D\u7684\u300D\u3092\u5358\u4F4D\u5143\u306E\u6709\u7121\u3092\u5F37\u8ABF\u3059\u308B\u610F\u5473\u3067\u306E\u307F\u7528\u3044\u308B\uFF08\u3064\u307E\u308A\u3001\u975E\u5358\u4F4D\u7684\u3067\u3042\u308B\u3068\u3044\u3063\u305F\u5834\u5408\u306B\u306F\u5B9F\u969B\u306B\u5358\u4F4D\u5143\u3092\u6301\u305F\u306A\u3044\uFF09\u3002"@ja . . . "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: /r\u028A\u014B/) 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 . . "\u62BD\u8C61\u4EE3\u6570\uFF0C\u4E00\u4E2A\u4F2A\u73AF\uFF08\u5373\u65E0\u4E58\u6CD5\u5355\u4F4D\u73AF\uFF09\u662F\u4EE3\u6570\u7ED3\u6784\u73AF\u7684\u7814\u7A76\u8FC7\u7A0B\u4E2D\uFF0C\u4E13\u6307\u65E0\u4E58\u6CD5\u5355\u4F4D\u5143\u7D20\u7684\u73AF\uFF0C\u201Crng\u201D \u4EE3\u8868\u6C92\u6709\u4E58\u6CD5\u5355\u4F4D\u5143\u7D20\uFF08\u82F1\uFF1A\"multiplicative identity\"\uFF09\u7684\u74B0\uFF08ring\uFF09\u3002"@zh . . . . . . "En matem\u00E1ticas 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 . \n* Datos: Q17102802"@es . . . . . . . . . . . . . "16460"^^ . . . "Rng (algebra)"@en . . . . . . . . . . "Pseudoanillo"@es . "3405004"^^ . . "En math\u00E9matiques, un pseudo-anneau est une des structures alg\u00E9briques utilis\u00E9es en alg\u00E8bre g\u00E9n\u00E9rale. C'est un ensemble muni d'une addition et d'une multiplication qui v\u00E9rifient les m\u00EAmes axiomes que celles d'un anneau, \u00E0 ceci pr\u00E8s qu'on n'exige pas la pr\u00E9sence d'un \u00E9l\u00E9ment neutre pour la multiplication. Une minorit\u00E9 d'auteurs ne demandent pas aux anneaux d'avoir un neutre multiplicatif ; si l'on se r\u00E9f\u00E8re \u00E0 leurs conventions, le pr\u00E9sent article traite donc de ce qu'ils appellent des anneaux."@fr . . . . . . . . . . . "\uD658\uB860\uC5D0\uC11C \uC720\uC0AC\uD658(\u985E\u4F3C\u74B0, \uC601\uC5B4: pseudoring \uB610\uB294 \uC601\uC5B4: rng [r\u028C\u014B])\uC740 \uD658\uACFC \uC720\uC0AC\uD558\uB098, \uACF1\uC148\uC5D0 \uB300\uD55C \uD56D\uB4F1\uC6D0\uC744 \uAC16\uC9C0 \uC54A\uC744 \uC218 \uC788\uB294 \uAD6C\uC870\uB2E4."@ko . . "En math\u00E9matiques, un pseudo-anneau est une des structures alg\u00E9briques utilis\u00E9es en alg\u00E8bre g\u00E9n\u00E9rale. C'est un ensemble muni d'une addition et d'une multiplication qui v\u00E9rifient les m\u00EAmes axiomes que celles d'un anneau, \u00E0 ceci pr\u00E8s qu'on n'exige pas la pr\u00E9sence d'un \u00E9l\u00E9ment neutre pour la multiplication. Une minorit\u00E9 d'auteurs ne demandent pas aux anneaux d'avoir un neutre multiplicatif ; si l'on se r\u00E9f\u00E8re \u00E0 leurs conventions, le pr\u00E9sent article traite donc de ce qu'ils appellent des anneaux. Il est possible d'ajouter une unit\u00E9 \u00E0 un anneau qui en est d\u00E9pourvu, ceci de plusieurs fa\u00E7ons. Dans une certaine mesure, ces techniques permettent d'utiliser la th\u00E9orie des anneaux unitaires pour traiter de questions concernant les pseudo-anneaux."@fr . . . . . . . . . . . . . . . . . . "\u4F2A\u73AF"@zh . "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: /r\u028A\u014B/) is meant to suggest that it is a ring without i, that is, without the requirement for an identity element. There is no consensus in the community as to whether the existence of a multiplicative identity must be one of the ring axioms (see Ring (mathematics) \u00A7 History). The term rng was coined to alleviate this ambiguity when people want to refer explicitly to a ring without the axiom of multiplicative identity. 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 . . "En matem\u00E1ticas 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 . \n* Datos: Q17102802"@es . . . . . . . . . "Pseudo-anneau"@fr . . . "\u64EC\u74B0"@ja . "\u62BD\u8C61\u4EE3\u6570\uFF0C\u4E00\u4E2A\u4F2A\u73AF\uFF08\u5373\u65E0\u4E58\u6CD5\u5355\u4F4D\u73AF\uFF09\u662F\u4EE3\u6570\u7ED3\u6784\u73AF\u7684\u7814\u7A76\u8FC7\u7A0B\u4E2D\uFF0C\u4E13\u6307\u65E0\u4E58\u6CD5\u5355\u4F4D\u5143\u7D20\u7684\u73AF\uFF0C\u201Crng\u201D \u4EE3\u8868\u6C92\u6709\u4E58\u6CD5\u5355\u4F4D\u5143\u7D20\uFF08\u82F1\uFF1A\"multiplicative identity\"\uFF09\u7684\u74B0\uFF08ring\uFF09\u3002"@zh . . . . . . "\u62BD\u8C61\u4EE3\u6570\u5B66\u306B\u304A\u3044\u3066\u5FC5\u305A\u3057\u3082\u5358\u4F4D\u5143\u3092\u6301\u305F\u306A\u3044\u74B0 (rng) \u3042\u308B\u3044\u306F\u64EC\u74B0\uFF08\u304E\u304B\u3093\u3001\u82F1: pseudo-ring\uFF09\u3001\u975E\u5358\u4F4D\u7684\u74B0\uFF08\u3072\u305F\u3093\u3044\u3066\u304D\u304B\u3093\u3001\u82F1: non-unital ring\uFF09\u306F\u3001\u4E57\u6CD5\u5358\u4F4D\u5143\u306E\u5B58\u5728\u4EE5\u5916\u306E\u74B0\u306E\u516C\u7406\u3092\u3059\u3079\u3066\u6E80\u305F\u3059\u3088\u3046\u306A\u4EE3\u6570\u7684\u69CB\u9020\u3092\u8A00\u3046\u3002\u82F1\u8A9E\u3067\u306F\u5C11\u3057\u304A\u3069\u3051\u3066\u3001\u300C\u5358\u4F4D\u5143\u300D\uFF08identity, \u3053\u308C\u3092\u3057\u3070\u3057\u3070 1 \u3067\u8868\u3059\uFF09\u306E\u7121\u3044\u300C\u74B0\u300D (ring) \u3060\u304B\u3089\u3068\u3044\u3046\u3053\u3068\u3067\u3001\u300Crng\u300D\u3068\u547C\u79F0\u3059\u308B\u3053\u3068\u3082\u3042\u308B\u3002 \u74B0\u306E\u516C\u7406\u306B\u4E57\u6CD5\u5358\u4F4D\u5143\u306E\u5B58\u5728\u3092\u542B\u3081\u306A\u3044\u6587\u732E\u3082\u3042\u308A\u3001\u3053\u306E\u6587\u8108\u3067\u306F\u672C\u9805\u306B\u4E91\u3046\u6982\u5FF5\u306F\u5358\u306B\u300C\u74B0\u300D\u3068\u547C\u79F0\u3055\u308C\u308B\u3002\u307E\u305F\u3001\u4FEE\u98FE\u8F9E\u300C\u975E\u5358\u4F4D\u7684\u300D\u306F\u300C\u5FC5\u305A\u3057\u3082\u5358\u4F4D\u7684\u3067\u306A\u3044\u300D\u3068\u3044\u3046\u610F\u5473\u3067\u7528\u3044\u3089\u308C\u308B\u304C\u3001\u672C\u9805\u3067\u306F\u305D\u306E\u610F\u5473\u3067\u306F\u5C02\u3089\u300C\u64EC\u74B0\u300D\u3092\uFF08\u3042\u308B\u3044\u306F\u76F4\u63A5\u7684\u306B\u300C\u5FC5\u305A\u3057\u3082\u300D\u3092\u4ED8\u3051\u3066\uFF09\u7528\u3044\u3001\u5358\u72EC\u306E\u300C\u5358\u4F4D\u7684\u300D\u30FB\u300C\u975E\u5358\u4F4D\u7684\u300D\u3092\u5358\u4F4D\u5143\u306E\u6709\u7121\u3092\u5F37\u8ABF\u3059\u308B\u610F\u5473\u3067\u306E\u307F\u7528\u3044\u308B\uFF08\u3064\u307E\u308A\u3001\u975E\u5358\u4F4D\u7684\u3067\u3042\u308B\u3068\u3044\u3063\u305F\u5834\u5408\u306B\u306F\u5B9F\u969B\u306B\u5358\u4F4D\u5143\u3092\u6301\u305F\u306A\u3044\uFF09\u3002"@ja . . . . . . . . . . "1107469419"^^ . . . . . . . . . "\uC720\uC0AC\uD658"@ko . . . .