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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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Applied General Topology, 2015 Suppose $F$ is a totally ordered field equipped with its order topology and $X$ a completely $F$-regular topological space. Suppose $\mathcal{P}$ is an ideal of closed sets in $X$ and $X$ is locally-$\mathcal{P}$.
Sudip Kumar Acharyya +2 more
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Some aspects in Noetherian modules and rings
AIMS Mathematics, 2022 Many authors have focused on the concept of Noetherian rings. M. Kosan and T. Quynh recently published an article on the Noetherian ring's new properties and their relation to the direct sum of injective hulls of simple right modules and essential ...
Nasr Anwer Zeyada, Makkiah S. Makki
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Homological Dimension in Noetherian Rings. [PDF]
Transactions of the American Mathematical Society, 1956 Introduction. Throughout this paper it is assumed that all rings are commutative, noetherian rings with unit element and all modules are unitary. The major purpose of this paper is to extend to arbitrary noetherian rings the homological invariants which were introduced in [2] for local rings.
Auslander, Maurice, Buchsbaum, David A.
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Integer-valued polynomials and binomially Noetherian rings
Zanco Journal of Pure and Applied Sciences, 2022 for each and i ≥ 0. The polynomial ring of integer-valued in rational polynomial is defined by Int ( an important example for binomial ring and is non-Noetherian ring. In this paper the algebraic structure of binomial rings has been studied by their
Shadman Kareem
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Pacific Journal of Mathematics, 1977 by a group of automorphisms of R. This paper explores what happens when the group is finite and the fixed ring S is assumed to be Noetherian Easy examples show that R may not be Noetherian; however, in this paper it is shown that R is Noetherian with some rather natural assuptions.
Farkas, Daniel R., Snider, Robert L.
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Ring Noetherian dan Ring Artinian
Sainsmat, 2014 DOWNLOAD PDF Dalam tulisan ini, diperkenalkan dua klas khusus dari ring yaitu Ring Noetherian dan Ring Artinian. Berawal dari adanya suatu ring komutatif yang mempunyai suatu ideal (ideal kiri dan ideal kanan). Apabila ideal tersebut
. Fitriani
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S-Noetherian rings, modules and their generalizations [PDF]
Surveys in Mathematics and its Applications, 2023 Let R be a commutative ring with identity, M an R-module and S ⊆ R a multiplicative set. Then M is called S-finite if there exist an s ∈ S and a finitely generated submodule N of M such that sM ⊆ N.
Tushar Singh +2 more
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Mathematics, 2020 Let R be a commutative ring with identity, and let S be a (not necessarily saturated) multiplicative subset of R. We define R to be a nonnil-S-Noetherian ring if each nonnil ideal of R is S-finite.
Min Jae Kwon, Jung Wook Lim
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Some Characterizations of w-Noetherian Rings and SM Rings
Journal of Mathematics, 2022 In this paper, we characterize w-Noetherian rings and SM rings. More precisely, in terms of the u-operation on a commutative ring R, we prove that R is w-Noetherian if and only if the direct limit of rGV-torsion-free injective R-modules is injective and ...
De Chuan Zhou +3 more
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