In this article, we define almost prime submodules as a new generalization of prime and
weakly prime submodules of unitary modules over a commutative ring with identity. We …

Essential Extensions of a Direct Sum of Simple Modules-II Page 1 Modules and Comodules
Trends in Mathematics, 243–246 c© 2008 Birkhäuser Verlag Basel/Switzerland Essential …

Recall that a commutative ring R is said to be a normal ring if it is reduced and every two
distinct minimal prime ideals are comaximal. A finitely generated reduced R-module M is …

Inspired by the interplay between the Zariski topology defined on the prime spectrum of a
commutative ring R and the ring theoretic properties of R in [3, 8, 18, 23, 25], we introduce in …

A fully invariant submodule of is called fully prime in if for fully invariant submodules and of,
implies or with. In this paper, we give some characterizations of fully prime submodules. We …

Let $ R $ be a commutative ring with identity and let $ M $ be an $ R $-module. A proper
submodule $ P $ of $ M $ is called strongly prime submodule if $(P+ Rx: M) y P $ for $ x, y M …

We develop a technique to construct finitely injective modules which are non-trivial, in the
sense that they are not direct sums of injective modules. As a consequence, we prove that a …

Prime and primary submodules of certain modules Page 1 Czechoslovak Mathematical Journal,
56 (131) (2006), 641–648 PRIME AND PRIMARY SUBMODULES OF CERTAIN MODULES …

Let $ R $ be a commutative ring with unity and $ K $ be a submodule of a non-zero left $ R $-
module $ D $. This paper introduces a new concept as a generalization of the prime …

PM Cohn [6] has defined the notion of a pure submodule. Subsequently CP Walker [21], B.
StenstrSm [19] and DP Choudhury and K. Tewari [5] have introduced notions of copurity as …