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Journal of MathematicsThe 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.
Rashid Abu-Dawwas +2 more
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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 ReportsThis 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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On graded nil clean rings [PDF]
Communications in Algebra, 2018 In this paper we introduce and study the notion of a graded (strongly) nil clean ring which is group graded. We also deal with extensions of graded (strongly) nil clean rings to graded matrix rings and to graded group rings. The question of when nil cleanness of the component, which corresponds to the neutral element of a group, implies graded nil ...
Emil Ilić-Georgijević
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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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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 +2 more
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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 +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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