Turkish Journal of Mathematics
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) \oplus S is T-noncosingular if and only if S is injective. Connections of T-noncosingular modules to their endomorphism rings are investigated.
Small submodules, T-noncosingular modules, endomorphism rings
"Some results on T-noncosingular modules,"
Turkish Journal of Mathematics: Vol. 38:
1, Article 4.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss1/4