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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
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.
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
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
On Graded Semiprime Submodules
Let G be an arbitrary group with identity e and let R be a G-graded ring. In this paper we define graded semiprime submodules of a graded R-module M and we give a number of results concerning such
Boolean Rings Obtained from Hyperrings with $$ \boldsymbol{\eta}_{1,m}^{\boldsymbol{*}} $$η1,m∗ Relations
The characterization of Boolean rings via strongly regular relations is investigated, and some properties on the topic are presented.
On graded hyperrings and graded hypermodules
Let G be a monoid with identity e. In this paper, first we introduce the notions of G-graded hyperrings, graded hyperideals and graded hyperfields in the sense of Krasner hyperring R. Also, we define
Finitely generated rings obtained from hyperrings through the fundamental relations
In this article, we introduce and analyze a strongly regular relation $\omega^{*}_{\mathcal{A}}$ on a hyperring$R$ such that in a particular case we have $|R/\omega^{*}_{\mathcal{A}}|\leq 2$