Some results on T -noncosingular modules

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 Jac(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 , E(S) ⊕ S is T -noncosingular if and only if S is injective. Connections of T -noncosingular modules to their endomorphism rings are investigated