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Reducibility of parameter ideals in low powers of the maximal ideal
Department of Mathematics, Gonzaga University, Spokane, 99258, WA, United States.
Department of Mathematics, Niagara University, Niagara, 14109, NY, United States .ORCID iD: 0000-0003-2714-9342
2021 (English)In: Contemporary Mathematics, vol 773, 2021, p. 181-193Conference paper, Published paper (Refereed)
Abstract [en]

A commutative noetherian local ring (R,m) is Gorenstein if and only if every parameter ideal of R is irreducible. Although irreducible parameter ideals may exist in non-Gorenstein rings, Marley, Rogers, and Sakurai show there exists an integer l (depending on R) such that R is Gorenstein if and only if there exists an irreducible parameter ideal contained in m^l. We give upper bounds for l that depend primarily on the existence of certain systems of parameters in low powers of the maximal ideal. 

Place, publisher, year, edition, pages
2021. p. 181-193
Keywords [en]
System of parameters, reducible parameter ideal, Gorenstein ring
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-64395DOI: 10.1090/conm/773/15541Scopus ID: 2-s2.0-85118684216ISBN: 9781470456016 (print)OAI: oai:DiVA.org:mdh-64395DiVA, id: diva2:1801343
Conference
2nd International Meeting on Commutative Algebra and Related Areas, SIMCARA 2019, and the AMS Special Session on Commutative Algebra, 2019, Madisson14 September 2019 through 15 September 2019
Available from: 2023-09-29 Created: 2023-09-29 Last updated: 2024-12-19Bibliographically approved

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