A generalizatio of injectivity for modules over a unitary ring

Ming, R.

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Tytuł artykułu

A generalizatio of injectivity for modules over a unitary ring

Autorzy

Ming R.

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http://www.degruyter.com/view/j/dema

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Abstrakty

In this note, we consider certain generalizations of injectivity and p-injectivity in connection with von Neumann regular rings, self-injective regular rings, I-regular rings, semi-simple Artinian and simple Artinian rings. A generalization of quasi-injective modules, noted SCS modules, is introduced. It is proved that A is a left self injective regular ring if, and only if, A is a left p-injective left non-singular left SCS ring. SCS rings are used to characterize simple Artinian rings. A generalization of p-injective modules, noted WGP-injective is used to study I-regular rings. If A is a right p.p. right WGP-injective ring, then A is I-regular. If A is a semi-prime ring whose simple left modules are either WGP-injective or projective, then the centre of A is von Neumann regular. Left Artinian rings are characterized as left Noetherian rings whose prime factor rings are left WGP-injective. Also, A is a left WGP-injective ring if and only if for any a is an element of A , there exists a positive integer n such that an A is a right anihilator. (Here an may be zero.)

Słowa kluczowe

injectivity SCS modules unitary ring Artinian rings VNR rings

odwzorowania moduły SCS pierścień unitarny pierścienie Artiniana pierścienie VNR

Wydawca

De Gruyter

Czasopismo

Demonstratio Mathematica

Rocznik

2006

Tom

Vol. 39, nr 4

Strony

759--770

Opis fizyczny

Bibliogr. 40 poz.

Twórcy

autor

Ming R.

Universite Paris VII-Denis Diderot UFR de Mathamatiques-UMR 9994 CNRS 2, Place Jussieu, 75 251 Paris Cedex 05, France

Bibliografia

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