On the arithmetic of stable domains

A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the rela...

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Detalles Bibliográficos
Autores principales: Bashir, Aqsa, Geroldinger, Alfred, Reinhart, Andreas
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Taylor & Francis 2021
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8404687/
https://www.ncbi.nlm.nih.gov/pubmed/34475609
http://dx.doi.org/10.1080/00927872.2021.1929275
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author Bashir, Aqsa
Geroldinger, Alfred
Reinhart, Andreas
author_facet Bashir, Aqsa
Geroldinger, Alfred
Reinhart, Andreas
author_sort Bashir, Aqsa
collection PubMed
description A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator property. In the present paper, we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains.
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spelling pubmed-84046872021-08-31 On the arithmetic of stable domains Bashir, Aqsa Geroldinger, Alfred Reinhart, Andreas Commun Algebra Research Article A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator property. In the present paper, we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains. Taylor & Francis 2021-06-30 /pmc/articles/PMC8404687/ /pubmed/34475609 http://dx.doi.org/10.1080/00927872.2021.1929275 Text en © 2021 The Author(s). Published with license by Taylor and Francis Group, LLC. https://creativecommons.org/licenses/by/4.0/This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Bashir, Aqsa
Geroldinger, Alfred
Reinhart, Andreas
On the arithmetic of stable domains
title On the arithmetic of stable domains
title_full On the arithmetic of stable domains
title_fullStr On the arithmetic of stable domains
title_full_unstemmed On the arithmetic of stable domains
title_short On the arithmetic of stable domains
title_sort on the arithmetic of stable domains
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8404687/
https://www.ncbi.nlm.nih.gov/pubmed/34475609
http://dx.doi.org/10.1080/00927872.2021.1929275
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