Results 21 to 30 of about 2,667 (226)
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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Some results on top local cohomology modules with respect to a pair of ideals [PDF]
Mathematica Bohemica, 2020 Let $I$ and $J$ be ideals of a Noetherian local ring $(R,\mathfrak m)$ and let $M$ be a nonzero finitely generated $R$-module. We study the relation between the vanishing of $H_{I,J}^{\dim M}(M)$ and the comparison of certain ideal topologies.
Saeed Jahandoust, Reza Naghipour
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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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On Semiprime Noetherian PI-Rings [PDF]
, 2000 Let R be a semiprime Noetherian PI-ring and Q(R) the semisimple Artinian ring of fractions of R. We shall prove the following conditions are equivalent: (1) the Krull dimention of R is at most one, (2) Any ring between R and Q(R) is again right ...
Chiba, Katsuo
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On nonnil-coherent modules and nonnil-Noetherian modules
Open Mathematics, 2022 In this article, we introduce two new classes of modules over a ϕ\phi -ring that generalize the classes of coherent modules and Noetherian modules. We next study the possible transfer of the properties of being nonnil-Noetherian rings, ϕ\phi -coherent ...
Haddaoui Younes El +2 more
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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
openaire +1 more source
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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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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Projective prime ideals and localisation in pi-rings [PDF]
, 2001 The results here generalise [2, Proposition 4.3] and [9, Theorem 5.11]. We shall prove the following. THEOREM A. Let R be a Noetherian PI-ring. Let P be a non-idempotent prime ideal of R such that PR is projective. Then P is left localisable and RP is
Chatters, A. W. +5 more
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FILTER REGULAR SEQUENCES AND LOCAL COHOMOLOGY MODULES [PDF]
Journal of Algebraic Systems, 2020 Let R be a commutative Noetherian ring. In this paper we consider some relations between filter regular sequence,regular sequence and system of parameters over R-modules.
J. Azami
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