Let R be a ring, M be a left R-module and Spec (RM) be the collection of all prime
submodules of M. In this paper and its sequel, we introduce and study a generalization of …

In this article, we give several generalizations of the concept of zero-divisor elements in a
commutative ring with identity to modules. Then, for each 𝑅-module 𝑀, we associate three …

Let M be a left R-module. In this paper a generalization of the notion of m-system set of rings
to modules is given. Then for a submodule N of M, we define\sqrt p N:= m ε M: every m …

In this paper we continue our study of classical Zariski topology of modules, that was
introduced in Part I (see [2]). For a left R-module M, the prime spectrum Spec (RM) of M is …

ON CHAINS OF CLASSICAL PRIME SUBMODULES AND DIMENSION THEORY OF
MODULES† Communicated by Siamak Yassemi 1. Introduction The cl Page 1 Bulletin of the …

On the prime spectrum of top modules Page 1 Algebra and Discrete Mathematics RESEARCH
ARTICLE Volume 11 (2011). Number 1. pp. 1 – 16 c Journal “Algebra and Discrete Mathematics” …

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 …

Here, we continue to characterize a recently introduced notion, le-modules RM over a
commutative ring R with unity [AK Bhuniya and M. Kumbhakar, Uniqueness of primary …

Let R be a commutative ring with nonzero identity and M be an R-module. Quasi-prime
submodules of M and the developed Zariski topology on q Spec (M) are introduced. We also …

Let R be a commutative ring with identity and let M be an R-module. A proper submodule P
of M is called a classical prime submodule if abm Î P for a, b Î R, and m Î M, implies that am Π…