Some results on T-noncosingular modules

Authors : Rachid TRIBAK

Pages : 29-39

Doi:10.3906/mat-1302-52

View : 16 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :The notion of T-noncosingularity of a module has been introduced and studied recently. In this article, a number of new results of this property are provided. It is shown that over a commutative semilocal ring R such that Jacinsert ignore into journalissuearticles values(R); is a nil ideal, every T-noncosingular module is semisimple. We prove that for a perfect ring R, the class of T-noncosingular modules is closed under direct sums if and only if R is a primary decomposable ring. Finitely generated T-noncosingular modules over commutative rings are shown to be precisely those having zero Jacobson radical. We also show that for a simple module S, Einsert ignore into journalissuearticles values(S); \oplus S is T-noncosingular if and only if S is injective. Connections of T-noncosingular modules to their endomorphism rings are investigated.
Keywords : Small submodules, T noncosingular modules, endomorphism rings