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Winter 2020 $\star$-super potent domains
Evan Houston, Muhammad Zafrullah
J. Commut. Algebra 12(4): 489-507 (Winter 2020). DOI: 10.1216/jca.2020.12.489

Abstract

For a finite-type star operation on a domain R, we say that R is -super potent if each maximal -ideal of R contains a finitely generated ideal I such that (1) I is contained in no other maximal -ideal of R and (2) J is -invertible for every finitely generated ideal JI. Examples of t-super potent domains include domains each of whose maximal t-ideals is t-invertible (e.g., Krull domains). We show that if the domain R is -super potent for some finite-type star operation , then R is t-super potent, we study t-super potency in polynomial rings and pullbacks, and we prove that a domain R is a generalized Krull domain if and only if it is t-super potent and has t-dimension one.

Citation

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Evan Houston. Muhammad Zafrullah. "$\star$-super potent domains." J. Commut. Algebra 12 (4) 489 - 507, Winter 2020. https://doi.org/10.1216/jca.2020.12.489

Information

Received: 19 September 2017; Revised: 10 December 2017; Accepted: 20 December 2017; Published: Winter 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194938
Digital Object Identifier: 10.1216/jca.2020.12.489

Subjects:
Primary: 13A05, 13A15
Secondary: 13F05, 13G05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 4 • Winter 2020
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