Projective module
In mathematics, particularly in abstract algebra and homological algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. A free module is a projective module, but the converse may be wrong over some rings, such as Dedekind rings. However, every projective module is a free module over a principal ideal domain, and over a polynomial ring over a field or the integers (this is Quillen–Suslin theorem).
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Projective module
In mathematics, particularly in abstract algebra and homological algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below. A free module is a projective module, but the converse may be wrong over some rings, such as Dedekind rings. However, every projective module is a free module over a principal ideal domain, and over a polynomial ring over a field or the integers (this is Quillen–Suslin theorem).
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Die projektive Dimension ist e ...... ils siehe Kommutative Algebra.
@de
En matemáticas, particularment ...... equivalentes de estos módulos.
@es
En mathématiques, un module pr ...... tient de N se factorise par N.
@fr
In matematica, un modulo proie ...... n e Samuel Eilenberg nel 1956.
@it
In mathematics, particularly i ...... i Cartan and Samuel Eilenberg.
@en
Проекти́вный мо́дуль — одно из ...... случаем проективных объектов.
@ru
在交換代數中，一個環 上的投射模是自由模的推廣，它有多種等價 ...... Algebra，由此定義的投射分解是同調代數的基本概念之一。
@zh
数学において、射影加群(しゃえいかぐん、英: project ...... 化に相当する。ホモロジー代数学における基本的な概念のひとつ。
@ja
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Die projektive Dimension ist e ...... ils siehe Kommutative Algebra.
@de
En matemáticas, particularment ...... equivalentes de estos módulos.
@es
En mathématiques, un module pr ...... tient de N se factorise par N.
@fr
In matematica, un modulo proie ...... n e Samuel Eilenberg nel 1956.
@it
In mathematics, particularly i ...... is is Quillen–Suslin theorem).
@en
Проекти́вный мо́дуль — одно из ...... случаем проективных объектов.
@ru
在交換代數中，一個環 上的投射模是自由模的推廣，它有多種等價 ...... Algebra，由此定義的投射分解是同調代數的基本概念之一。
@zh
数学において、射影加群(しゃえいかぐん、英: project ...... 化に相当する。ホモロジー代数学における基本的な概念のひとつ。
@ja
label
Module projectif
@fr
Modulo proiettivo
@it
Módulo proyectivo
@es
Projective module
@en
Projektive Dimension
@de
Проективный модуль
@ru
射影加群
@ja
投射模
@zh
