ON AUTOMORPHISM-INVARIANT MULTIPLICATION MODULES OVER A NONCOMMUTATIVE RING

. One of the important classes of modules is the class of multiplication modules over a commutative ring. This topic has been considered by many authors and numerous results have been obtained in this area. After that, Tuganbaev also considered the multiplication module over a noncommutative ring. In this paper, we continue to consider the automorphism-invariance of multiplication modules over a noncommutative ring. We prove that if R is a right duo ring and M is a multiplication, finitely generated right R-module with a generating set {m1, ... , mn} such that r(mi) = 0 and [miR : M] subset of C(R) the center of R, then M is projective. Moreover, if R is a right duo, left quasi-duo, CMI ring and M is a multiplication, non-singular, automorphism-invariant, finitely generated right R-module with a generating set {m1, ... , mn} such that r(mi) = 0 and [miR : M] subset of C(R) the center of R, then MR similar to= R is injective.