With the notion of prime submodule defined by F. Raggi et. al. we prove that the intersection
of all prime submodules of a Goldie module $ M $, is a nilpotent submodule provided that …

Using the concepts of prime module, semiprime module and the concept of ascending chain
condition (ACC) on annihilators for an R-module M, we prove that if M is semiprime and …

For an R-module M, projective in σ [M] and satisfying ascending chain condition on left
annihilators, the authors introduce the concept of Goldie module. The authors also use the …

NONSINGULAR EXTENDING MODULES Page 1 NONSINGULAR EXTENDING MODULES
PATRICK F. SMITH ABSTRACT. In this paper, it is shown that if R is a semiprime right Goldie …

A right R-module M is called a Goldie module if it has finite Goldie dimension and satisfies
the ACC for M-annihilator submodules of M. In this paper, we study the class of prime Goldie …

The purpose of the present paper is to prove some properties of the strongly irreducible
submodules in the arithmetical and Noetherian modules over a commutative ring. The …

It is shown that a ring R is semiprime right Goldie if and only if R is right nonsingular and
every nonsingular right R-module M has a direct decomposition M= I⊕ N, where I is injective …

We prove that if R is an idempotent reflexive left Goldie ring whose simple singular left R-
modules are GP-injective, then R is a finite product of simple left Goldie rings. As a …

In this article, we study the second radical of a module over an arbitrary ring R as the dual
notion of the prime radical of a module. We give some properties of the second radical and …

Using the concept of prime submodule introduced by Raggi et. al. we extend the notion of
reduced rank to the module-theoretic context. We study the quotient category of $\sigma [M] …