Results 11 to 20 of about 30,010 (264)

When Are Graded Rings Graded S-Noetherian Rings [PDF]

Mathematics, 2020
Let Γ be a commutative monoid, R=⨁α∈ΓRα a Γ-graded ring and S a multiplicative subset of R0. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian
Dong Kyu Kim, Jung Wook Lim
doaj   +2 more sources

The free A-ring is a graded A-ring [PDF]

International Journal of Mathematics and Mathematical Sciences, 1993
In this paper, we define the free A-ring over K on a set X, categorically, and parallel some results from the theory of free algebras. We show that the free A-ring over K on X, denoted by AK{X}, is graded.
Roger D. Warren
doaj   +2 more sources

EM− Graded Rings

Journal of Mathematics
The main goal of this article is to introduce the concept of EM−G− graded rings. This concept is an extension of the notion of EM− rings. Let G be a group, and R be a G− graded commutative ring.
Tariq Alraqad, Hicham Saber, Rashid Abu-Dawwas   +2 more
doaj   +3 more sources

Rings Graded By a Generalized Group

Topological Algebra and its Applications, 2014
The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups.We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. Weprove that if I is a complete homogeneous ideal of a G-
Fatehi Farzad, Molaei Mohammad Reza
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GRADED I-PRIME SUBMODULES [PDF]

Journal of Algebraic Systems, 2023
Let $R= \bigoplus_{g \in G} R_g$ be a $G-$graded commutative ring with identity, $I$ be a graded ideal and let $M$ a $G-$graded unitary $R$-module, where $G$ is a semigroup with identity $e$.
I. Akray, Sh. Othman, A. Jabbar, H. Hussein   +3 more
doaj   +1 more source

On Graded 2-Prime Ideals

Mathematics, 2021
The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different.
Malik Bataineh, Rashid Abu-Dawwas
doaj   +1 more source

Brown-McCoy Radical in Restricted Graded Version

JTAM (Jurnal Teori dan Aplikasi Matematika), 2022
Some conjectures related to the radical theory of rings are still open. Hence, the research on the radical theory of rings is still being investigated by some prominent authors.
Puguh Wahyu Prasetyo
doaj   +1 more source

Graded weakly 1-absorbing prime ideals

Cubo, 2022
In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let $G$ be a group and $R$ be a $G$-graded commutative ring with a nonzero identity $1\neq0$.
Ünsal Tekir, Suat Koç, Rashid Abu-Dawwas, Eda Yıldız   +3 more
doaj   +1 more source

On properties of graded rings and graded modules

Proyecciones (Antofagasta), 2022
Let R be a G-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded rings. Also, we study the concept of weakly crossed products and study some properties defined on weakly crossed product ...
Refai, Mashhoor, Abu-Dawwas, Rashid
openaire   +3 more sources

Some properties of graded generalized 2-absorbing submodules

Demonstratio Mathematica, 2022
Let GG be an abelian group with identity ee. Let RR be a GG-graded commutative ring and MM a graded RR-module. In this paper, we will obtain some results concerning the graded generalized 2-absorbing submodules and their homogeneous components.
Alghueiri Shatha, Al-Zoubi Khaldoun
doaj   +1 more source