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HOMOLOGICAL DIMENSION IN NOETHERIAN RINGS. [PDF]
Proc Natl Acad Sci U S A, 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 M, Buchsbaum DA.
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Local rings with noetherian filtrations [PDF]
Pacific Journal of Mathematics, 1971 Chin-Pi Lu
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A COUNTEREXAMPLE IN NOETHERIAN RINGS. [PDF]
Proc Natl Acad Sci U S A, 1965 Herstein IN.
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AN EXAMPLE IN NOETHERIAN RINGS. [PDF]
Proc Natl Acad Sci U S A, 1965 Small LW.
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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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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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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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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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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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