It is shown that if every prime ideal minimal over an ideal I is finitely generated, then there
are only finitely many prime left ideals minimal over I. This immedeately generalizes Cohen's …

Minimal Prime Submodules 1 Introduction 2 The results Page 1 International Journal of
Algebra, Vol. 2, 2008, no. 20, 953 - 956 Minimal Prime Submodules Atul Gaur and Alok Kumar …

Let R be a commutative ring with identity and M be an R-module. As a new generalization of
primary ideals to modules, a proper submodule N of M is a primary-like submodule if …

Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime
submodule of M is defined. It is shown that this notion of prime submodule inherits most of …

Let R be any ring and M an R-module. For any submodule N of M, let (N: M) denote the set
of elements r in R such that rM C N. Note that (N: M) is the annihilator of the module M/N …

The Principal Ideal Theorem states that if Re is a commutative Noetherian ring and? is a
prime ideal of Re which is minimal over a principal ideal then Pe has height at most 1. Also …

Let R be a commutative ring with unity and let M be a left R-module. We define a proper
submodule N of M to be a weakly prime if whenever r &# 61646; R, x &# 61646; M, 0 &# …

Our main aim in this note, is a further generalization of a result due to DD Anderson, ie, it is
shown that if R is a commutative ring, and M a multiplication R-module, such that every …

A proper submodule N of a module M over a ring R is said to be prime (or P-prime) if re e N
for re R and ee M implies that either ee N or re P= N: M. In other words, N is a prime …

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 …