In this article, we introduce the dual notions of strongly prime, weakly prime, semiprime, and
primal submodules, that is, strongly second, weakly second, semisecond, and secondal …

Let R be a commutative ring with identity and all modules are unital. Various generalizations
of primary ideals and primary modules have been studied. For example, a proper ideal I of R …

In this paper we introduce the notion of classical quasi PRIMARY submodules that
generalizes the concept of classical PRIMARY submodules. Then, we investigate …

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

Abstract In [10, 11] the concept of modules satisfying dccr was introduced and developed. In
this note the prime (resp. weakly prime) submodules of this class of modules is …

It is known that every semiprime ring is a subdirect sum of prime rings. This is a
consequence of the fact that every semiprime ideal is an intersection of prime ideals. We aim …

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∈ P for a, b∈ R, and m∈ M, implies that …

We will state some conditions under which if a quotient of a module M satisfies the radical
formula of degree k (strf of degree k), so does M. Especially, we will introduce some …

In this paper, the notation of prime-extending module, is introduced and studied where an R-
module M is Prime-extending if every nonzero proper submodule of M is essential in prime …

Height of Prime and Weakly Prime Submodules Page 1 Mediterr. J. Math. 8 (2011), 257–269
DOI 10.1007/s00009-010-0068-6 1660-5446/11/020257-13, published online May 1, 2010 © …