Journal Article10.12988/IJA.2013.13003
Multiplication Graded Modules
A. Khaksari,F. Rasti Jahromi +1 more
TL;DR: In this article, various properties of multiplicative ideals in a graded ring are discussed and the set of P -primary ideals and modules of R when P is a graded multiplication prime ideal and modules.
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Abstract: Let G be a multiplicative group and R be a G -graded commutative ring and M a G -graded R -module. Various properties of multiplicative ideals in a graded ring are discussed and we extend this to graded modules over graded rings. We have also discussed the set of P -primary ideals and modules of R when P is a graded multiplication prime ideals and modules.
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Citations
Graded generalized 2-absorbing submodules
Rashid Abu-Dawwas,Malik Bataineh,Heba Shashan +2 more
- 01 Dec 2021
TL;DR: In this paper, the concept of graded generalized 2-absorbing submodules was introduced, which is a generalization of graded 2 absorbing submodules, and investigated some properties of this new class of graded submodules.
7
Intersection graphs of graded ideals of graded rings
Tariq Alraqad,Hicham Saber,Rashid Abu-Dawwas +2 more
- 01 Jan 2021
TL;DR: In this article, the intersection graph of graded ideals of a graded ring is studied and properties such as connectivity, regularity, completeness, domination numbers, and girth are studied.
5
Graded weak comultiplication modules
TL;DR: In this article, the concept of graded weak comultiplication modules was introduced, where a module is said to be a weak module if for every graded prime $R$-submodule $N$ of a module of a group with identity $e, the ideal module of the group is a submodule of some graded ideal module.
3
On generalizations of graded multiplication modules
TL;DR: In this paper , the authors introduce the concept of graded quasi multiplication modules and graded absorbing multiplication modules for weakly prime submodules and graded 2-absorbing submodules, respectively.
2
Graded semiprime multiplication modules
Rashid Abu-Dawwas
- 01 Jan 2021
TL;DR: In this article, the concept of graded semiprime multiplication modules is introduced and several results concerning the performance of G-graded R-module submodules are investigated. But these results are restricted to the case where the submodules have no graded semi-modal R-submodules.
References
Multiplication modules and theorems of mori and mott
TL;DR: In this article, the authors present the Multiplication modules and theorems of mori and mott for algebraic multiplication modules and derive theorem 1.1.2.
158
•Journal Article
On Graded Primary Ideals
Mashhoor Refai,Khaldoun Al-Zoubi +1 more
TL;DR: In this article, the graded primary ideals and graded primary G-decomposition of a graded ideal are studied, where G is a group and R is a G-graded commutative ring.
87
On the prime submodules of multiplication modules
TL;DR: In this paper, the notion of multiplication modules over a commutative ring with identity was introduced, and the product of two submodules of such modules was characterized by the Nakayama lemma.