Characterization and examples of commutative iso-Artinian rings
Daneshvar, Asghar (Alzahra University (Teheran, Iran). Department of Mathematics)
Divaani-Aazar, Kamran (Alzahra University (Teheran, Iran). Department of Mathematics)

Date:	2025
Abstract:	Noetherian rings have played a fundamental role in commutative algebra, algebraic number theory, and algebraic geometry. Along with their dual, Artinian rings, they have many generalizations, including the notions of iso-Noetherian and iso-Artinian rings. In this paper, we prove that the Krull dimension of every iso-Artinian ring is at most one. We then use this result to provide a characterization of iso-Artinian rings. Specifically, we prove that a ring R is iso-Artinian if and only if R is uniquely isomorphic to the direct product of a finite number of rings of the following types: (i) Artinian local rings; (ii) non-Noetherian iso-Artinian local rings with a nilpotent maximal ideal; (iii) non-field principal ideal domains; (iv) Noetherian iso-Artinian rings A with Min A being a singleton and Min A ( Ass A; (v) non-Noetherian iso-Artinian rings A with Min A being a singleton and Min A ( Ass A; (vi) non-Noetherian iso-Artinian rings A with a unique element in Min A that is not maximal, and Min A = Ass A. Several examples of these types of rings are also provided.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Dedekind ring ; Iso-artinian ring ; Marot ring ; Perfect ring ; Principal ideal domain ; Prüfer ring ; Subperfect ring
Published in:	Publicacions matemàtiques, Vol. 69 Núm. 2 (2025) , p. 403-414 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/10000006144
DOI: 10.5565/PUBLMAT6922507

12 p, 314.7 KB

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