Rings with an elementary abelian $p$-group of units
Commutative Algebra
2023-01-02 v2 Rings and Algebras
Abstract
What are all rings for which (the group of invertible elements of under multiplication) is an elementary abelian -group? We answer this question for finite-dimensional commutative -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.
Cite
@article{arxiv.2112.03853,
title = {Rings with an elementary abelian $p$-group of units},
author = {Sunil K. Chebolu and Jeremy Corry and Elizabeth Grimm and Andrew Hatfield},
journal= {arXiv preprint arXiv:2112.03853},
year = {2023}
}
Comments
11 pages, 1 figure, to appear in the Journal of Commutative Algebra