Throughout this paper, $ R $ is an associative ring (not necessarily commutative) with
identity and $ M $ is a right $ R $-module with unitary. In this paper, we introduce a new …

Recall that a ring R is said to be a quasi regular ring if its total quotient ring q (R) is von
Neumann regular. It is well known that a ring R is quasi regular iff it is a reduced ring …

In this paper, we study the concepts of n-absorbing and weakly n-absorbing submodules of
modules over a commutative ring with non-zero unity which is a generalization of prime and …

All rings are assumed to be associative and with nonzero identity element. Unless otherwise
stated all modules are unital right modules. Expressions such as “a Noetherian ring” mean …

This paper examines the radical formula in noncommutative case and for this purpose, a
generalization of prime submodule is defined. It is proved that there is a direct connection …

ON THE PRIMARY AVOIDANCE THEOREM FOR MODULES OVER COMMUTATIVE RINGS
Throughout this paper, R denotes a commutative ring with ide Page 1 ON THE PRIMARY …

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of
prime submodules (that is, second submodules of M) and investigate the conditions under …

Let R be a commutative ring with unity. M an R-Module. M is called coprime module (dual
notion of prime module) if ann M= ann M/N for every proper submodule N of M In this paper …

Let R be a commutative ring with identity and M an R–module. If M is either locally cyclic
projective or faithful multiplication then M is locally either zero or isomorphic to R. We …