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Preprint . 2021
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Article . 2023
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Journal of Commutative Algebra
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Article . 2021
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RINGS WITH AN ELEMENTARY ABELIAN p-GROUP OF UNITS

Rings with an elementary abelian \(p\)-group of units
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2023Embargo end date: 01 Jan 2021Publisher:Rocky Mountain Mathematics ConsortiumJournal:Journal of Commutative Algebra, volume 15 (issn: 1939-2346, Copyright policy )
Authors: Chebolu, Sunil K.; Corry, Jeremy; Grimm, Elizabeth; Hatfield, Andrew;

doi: 10.1216/jca.2023.15.469 , 10.48550/arxiv.2112.03853

arXiv: 2112.03853

RINGS WITH AN ELEMENTARY ABELIAN p-GROUP OF UNITS

Abstract

What are all rings $R$ for which $R^*$ (the group of invertible elements of $R$ under multiplication) is an elementary abelian $p$-group? We answer this question for finite-dimensional commutative $k$-algebras, finite commutative rings, modular group algebras, and path algebras. Two interesting byproducts of this work are a characterization of Mersenne primes and a connection to Dedekind's problem.

11 pages, 1 figure, to appear in the Journal of Commutative Algebra

Keywords

Units, groups of units (associative rings and algebras), group algebras, local rings, 11T06, 16U60, Mathematics - Rings and Algebras, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Wedderburn-Artin, Primes, group of units, Rings and Algebras (math.RA), FOS: Mathematics, Structure of finite commutative rings, commutative rings

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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