• Publications
  • Influence
On weakly prime submodules
Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $ of an $ R $-module $ M $ to be weakly prime if $ 0\not = rm\in N $( $ r\in R, m\in M $) implies $ m\in N $
On Weakly Primary Ideals
Abstract Weakly prime ideals in a commutative ring with non-zero identity have been introduced and studied in Anderson and Smith, Houston J. Math. 29: 831840, 2003. Here we study the weakly primary
On the Union of Graded Prime Submodules
Let G be a group with identity e . Let R be a G -graded commutative ring, and let M be a graded R -module. In this paper, we investigate finite and infinite union of graded submodules of a graded R
On Graded Secondary Modules
Let G be a group with identity e ,a nd letR be a G-graded commutative ring. Here we study the graded primary submodules of a G-graded R-module and examine when graded submodules of a graded
Notes on the Union of Weakly Primary Submodules
Let 𝑅 be a commutative ring with identity, and let 𝑀 be an 𝑅-module. A proper submodule 𝑁 of 𝑀 is said to be weakly primary if 0≠𝑟𝑚∈𝑁 for 𝑟∈𝑅 and 𝑚∈𝑀, which implies that either 𝑚∈𝑁 or
On graded weak multiplication modules
Let $G$ be a group with identity $e$, and let $R$ be a $G$-graded commutative ring, and let $M$ be a graded $R$-module. In this paper we characterize graded weak multiplication modules.
ON GRADED SEMIPRIME AND GRADED WEAKLY SEMIPRIME IDEALS
Let G be an arbitrary group with identity e and let R be a Ggraded ring. In this paper, we define graded semiprime ideals of a commutative G-graded ring with nonzero identity and we give a number of
Weak multiplication modules over a pullback of Dedekind domains
Let R be the pullback, in the sense of Levy [J. Algebra 71 (1981)], of two local Dedekind domains. We classify all those indecomposable weak multiplication R-modules M with finite-dimensional top,
On Almost Semiprime Submodules
We introduce the concept of almost semiprime submodules of unitary modules over a commutative ring with nonzero identity. We investigate some basic properties of almost semiprime and weakly
Generalization of Semiprime Subsemimodules
The authors introduce the concept of almost semiprime subsemimodules of semimodules over a commutative semiring R . They investigated some basic properties of almost semiprime and weakly semiprime
...
...