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Demonstratio Mathematica

Tytuł artykułu

A generalizatio of injectivity for modules over a unitary ring

Autorzy Ming, R. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
EN 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
PL odwzorowania   moduły SCS   pierścień unitarny   pierścienie Artiniana   pierścienie VNR  
EN injectivity   SCS modules   unitary ring   Artinian rings   VNR rings  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2006
Tom Vol. 39, nr 4
Strony 759--770
Opis fizyczny Bibliogr. 40 poz.
autor Ming, R.
  • Universite Paris VII-Denis Diderot UFR de Mathamatiques-UMR 9994 CNRS 2, Place Jussieu, 75 251 Paris Cedex 05, France
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