Results 11 to 20 of about 186 (173)
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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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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On multiplication $fs$-modules and dimension symmetry [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we first study $fs$-modules, i.e., modules with finitely many small submodules. We show that every $fs$-module with finite hollow dimension is Noetherian.
Nasrin Shirali +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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On the properties of weak CM rings
上海师范大学学报. 自然科学版, 2022 In this paper, we mainly study the properties of weak CM rings. It is a special class of Noetherian commutative rings, including Cohen-Macaulay rings, excellent rings and generalized Cohen-Macaulay rings, which can be characterized by local cohomology ...
XUE Wensi, ZHOU Caijun
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On stable noetherian rings [PDF]
Transactions of the American Mathematical Society, 1975 A ring R is called stable if every localizing subcategory of R
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On Noetherianness of Nash rings [PDF]
Proceedings of the American Mathematical Society, 1984 We introduce a class of rings, called Nash Rings, which generalize the notation of rings of Nash functions. Let k k be any field, X X be a normal algebraic variety in k n {k^n} , and U ⊂ X U \subset X .
Mora, Fulvio, Raimondo, Mario
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On the Ring of Quotients of a Noetherian Ring [PDF]
Canadian Mathematical Bulletin, 1965 This paper is largely an expository account of known facts, but it contains at least one result believed to be new, Proposition 6.Our main technique is the method of lifting idempotents developed in Part I. This has been treated in the literature, but not quite in the generality required here.
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When Are Graded Rings Graded S-Noetherian Rings
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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A theorem on Noetherian hereditary rings [PDF]
Pacific Journal of Mathematics, 1973 It is shown (Theorem 2) that a semi-prime, left noetherian, left hereditary, two-sided Goldie ring is right noetherian if and only if the right module (Q/R) φ R contains a copy of every simple right iέ-module, where Q is the classical quotient ring of R.
Camillo, Victor P., Cozzens, J.
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