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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
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Bandgap characteristics and optimization of two-dimensional phononic metamaterials with functionally graded rings [PDF]

Scientific Reports
This paper systematically investigates the influence of the thickness and power-law exponent of functionally graded rings (FGR) on the bandgap characteristics of two-dimensional (2D) phononic metamaterials (PMs). Based on the plane wave expansion method (
Qiangqiang Li, Jingya Wang
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Lim Ulrich sequences and Boij-Söderberg cones

Forum of Mathematics, Sigma, 2023
This paper extends the results of Boij, Eisenbud, Erman, Schreyer and Söderberg on the structure of Betti cones of finitely generated graded modules and finite free complexes over polynomial rings, to all finitely generated graded rings admitting linear ...
Srikanth B. Iyengar, Linquan Ma, Mark E. Walker   +2 more
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Graded Derived Equivalences

Mathematics, 2021
We consider the equivalences of derived categories of graded rings over different groups. A Morita type equivalence is established between two graded algebras with different group gradings.
Bo-Ye Zhang, Ji-Wei He
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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
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ON GRADED INJECTIVE DIMENSION [PDF]

Journal of Algebraic Systems, 2019
There are remarkable relations between the graded homological dimensions and the ordinary homological dimensions. In this paper, we study the injective dimension of a complex of graded modules and derive its some properties. In particular, we define the $
Akram Mahmoodi, Afsaneh Esmaeelnezhad
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Acyclic Complexes and Graded Algebras

Mathematics, 2023
We already know that the noncommutative N-graded Noetherian algebras resemble commutative local Noetherian rings in many respects. We also know that commutative rings have the important property that every minimal acyclic complex of finitely generated ...
Chaoyuan Zhou
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On Properties of Graded Rings with respect to Group Homomorphisms

International Journal of Mathematics and Mathematical Sciences, 2023
Let G be a group and R be a G-graded ring with non-zero unity. The goal of our article is reconsidering some well-known concepts on graded rings using a group homomorphism α:G⟶G. Next is to examine the new concepts compared to the known concepts.
Azzh Saad Alshehry, Rashid Abu-Dawwas, Muhsen Al-Bashayreh   +2 more
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On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings

Demonstratio Mathematica, 2021
Let G be an abelian group with identity ee. Let R be a G-graded commutative ring with identity 1, and MM be a graded R-module. In this paper, we introduce the concept of graded Jgr{J}_{gr}-classical 2-absorbing submodule as a generalization of a graded ...
Al-Zoubi Khaldoun, Alghueiri Shatha
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K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories [PDF]

Categories and General Algebraic Structures with Applications, 2022
We build on previous work on multirings ([17]) that providesgeneralizations of the available abstract quadratic forms theories (specialgroups and real semigroups) to the context of multirings ([10], [14]).
Kaique Roberto, Hugo Mariano
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