Results 161 to 170 of about 310,219 (199)

A note on a class of Noetherian rings

, 1975
Kumar, R., Manaktala, K.
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On Right S-Noetherian Rings and S-Noetherian Modules [PDF]

Communications in Algebra, 2018
In this paper we study right S-Noetherian rings and modules, extending notions introduced by Anderson and Dumitrescu in commutative algebra to noncommutative rings.
Manuel Lionel Reyes, Unsal Tekir
exaly   +3 more sources

A Note on Weakly S-Noetherian Rings

Symmetry, 2020
Let R be a commutative ring with identity and S a (not necessarily saturated) multiplicative subset of R. We call the ring R to be a weakly S-Noetherian ring if every S-finite proper ideal of R is an S-Noetherian R-module.
Jung Wook Lim, Dong Kyu Kim
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On serial noetherian rings

Archiv der Mathematik, 1991
\textit{S. Singh} [Arch. Math. 39, 306-311 (1982; Zbl 0502.16012)] considered rings \(R\) with the property: (P) every finitely generated right \(R\)-module is a direct sum of a projective module with zero socle and uniserial Artinian modules. He proved that a right FBN-ring satisfying (P) is a direct sum of an Artinian serial ring and right hereditary
Dinh Van Huynh, Phan Dan
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Noetherian biserial rings

Ukrainian Mathematical Journal, 1989
See the review in Zbl 0661.16009.
Kirichenko, V. V., Yaremenko, Yu. V.
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Meta-noetherian rings

ANNALI DELL UNIVERSITA DI FERRARA, 1976
Noi introduciamo degli invarianti numerici per misurare in diverse maniere quanto manchi ad un anello per essere noetheriano. La classe degli anelli meta-Noetheriani gode di proprieta ragionevoli. Noi studiamo in particolare il loro comportamento per passaggio all'anello di polinomi.
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Ideal Decompositions in Noetherian Rings

Canadian Journal of Mathematics, 1965
An interesting identity is obtained for ideals A and B in a Noetherian ring :A = (A + Bn) ∩ (A : Bn)for sufficiently large n. This identity is applied to obtain Fuchs' quasi-primary decomposition of A in an improved form, and to obtain Krull's theorem on the intersection of the powers of A, both developments making no use of the Noetherian primary ...
Barnes, Wilfred E., Cunnea, William M.
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On strongly J-Noetherian rings

Journal of Algebra and Its Applications, 2021
In this paper, we introduce a class of commutative rings which is a generalization of [Formula: see text]-rings and rings with Noetherian spectrum. A ring [Formula: see text] is called strongly [Formula: see text]-Noetherian whenever the ring [Formula: see text] is [Formula: see text]-Noetherian for every non-nilpotent [Formula: see text].
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Characterizations of generalized noetherian rings

Acta Mathematica Hungarica, 1989
A ring with several objects is a small additive category \({\mathcal C}\). In this setting, the role of the module category is played by the category \(Ab^{{\mathcal C}}\) of additive functors \({\mathcal C}\to Ab\). Extending results of the first author [Acta Math. Acad. Sci. Hung.
Hannick, Francis T., Hewitt, Gloria C.
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A Condition for Artinian Rings to be Noetherian

Canadian Journal of Mathematics, 1978
Throughout this paper the word “Artinian (Noetherian) ring” means an associative ring with minimum (maximum) condition on left ideals. According to C. Hopkins, an Artinian ring is Noetherian if it contains a left or right identity [3, p. 728]. However we shall consider Artinian rings without the assumption of existence of such an identity, and the ...
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