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arXiv · 2112.03853

Rings with an elementary abelian $p$-group of units

Sunil K. Chebolu·Jeremy Corry·Elizabeth Grimm·Andrew Hatfield
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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.

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Sunil K. Chebolu, Jeremy Corry, Elizabeth Grimm, Andrew Hatfield. 2021-12-07. Rings with an elementary abelian $p$-group of units. https://arxiv.org/abs/2112.03853

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