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CORETRACTABLE MODULES

Part of: Local rings and generalizations Modules, bimodules and ideals

Published online by Cambridge University Press:  01 June 2009

B. AMINI ,
M. ERSHAD  and
H. SHARIF
B. AMINI*
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran (email: bamini@shirazu.ac.ir)
M. ERSHAD
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran (email: ershad@shirazu.ac.ir)
H. SHARIF
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran (email: sharif@susc.ac.ir)
*
✉For correspondence; e-mail: bamini@shirazu.ac.ir
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Abstract

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An R-module M is called coretractable if  HomR(M/K,M)≠0 for any proper submodule K of M. In this paper we study coretractable modules and their endomorphism rings. It turns out that if all right R-modules are coretractable, then R is a right Kasch and (two-sided) perfect ring. However, the converse holds for commutative rings. Also, for a semi-injective coretractable module MR with S=EndR(M), we show that u.dim(SS)=corank(MR).

Keywords

coretractable moduleKasch ringperfect ringsemi-Artinian ringmax ringsemi-injective module

MSC classification

Secondary: 16D10: General module theory 16L30: Noncommutative local and semilocal rings, perfect rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 3 , June 2009 , pp. 289 - 304
Copyright
Copyright © Australian Mathematical Society 2009

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