Finitely generated graded multiplication modules
TL;DR: In this article, it was shown that any graded submodule of a finitely generated generalised graded multiplication R-module M has a kind of primary decomposition, and a characterisation of graded primary submodules of M was given.
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Abstract: Let R = ⊕i ∈ ℤRi be a ℤ-graded ring and M = ⊕i ∈ ℤMi be a graded R-module. Providing some results on graded multiplication modules, some equivalent conditions for which a finitely generated graded R-module to be graded multiplication will be given. We define generalised graded multiplication module and determine some of its certain graded prime submodules. It will be shown that any graded submodule of a finitely generated generalised graded multiplication R-module M has a kind of primary decomposition. Using this, we give a characterisation of graded primary submodules of M. These lead to a kind of characterisation of finitely generated generalised graded multiplication modules.
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Citations
Some properties of graded comultiplication modules
TL;DR: In this paper, the graded comultiplication modules over a commutative graded ring were investigated and the authors obtained some results concerning the graded COMPLIATION modules over the graded ring.
On graded quasi-primary submodules of graded modules over graded commutative rings
Khaldoun Al-Zoubi,Rweili Alkhalaf +1 more
- 01 Jan 2021
TL;DR: In this article, the authors introduce the concept of graded quasi-primary submodules of graded modules over graded commutative rings, and consider various properties of these submodules, e.g., the properties of a given submodal group with identity.
On graded $S$-comultiplication modules
Mohammad Hamoda,Khaldoun Al-Zoubi +1 more
- 28 Apr 2022
TL;DR: In this article , the concept of graded S − comultiplication modules was introduced, and several results concerning graded S-commodity modules were proved. But these results depend on the assumption that the S − prime ideal of R is known and there exists a submodule of R such that xN ⊆ xN for every x ∈ S .
FINITELY GENERATED gr-MULTIPLICATION MODULES
Seungkook Park
- 15 Nov 2012
TL;DR: In this paper, it was shown that if M is a finitely generated gr-multiplication R-module, then there is a lattice isomorphism between the lattice of all graded ideals I of R containing ann(M) and the lattices of all submodules of M.
On graded $S$-comultiplication modules
28 Apr 2022
TL;DR: In this article , the concept of graded $S$-comultiplication modules was introduced and several results concerning graded S$-COMPLIMATION modules were proved, such as the following:
References
•Book
Commutative Ring Theory
Hideyuki Matsumura,Miles Reid +1 more
- 30 Jun 1989
TL;DR: In this article, the authors introduce the notion of complete local rings and apply it to a wide range of applications, including: I-smoothness, I-flatness revisited, and valuation rings.
4.7K
•Book
Cohen-Macaulay rings
Winfried Bruns,H. Jürgen Herzog +1 more
- 01 Jan 1993
TL;DR: In this article, the authors present a self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules.
3.3K
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