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- W2467176698 abstract "In cite[Problem 72]{Fuchs60} Fuchs asked the following question: which abelian groups can be the group of units of a ring? In the years, some partial answers have been given to this question in particular cases. The aim of the present paper is to address Fuchs' question when $A^*$ is a {it finite abelian group}. The result is a pretty good description of the finite abelian groups which can occur as group of units of a ring, equipped with examples showing that there are obstacles to a short complete classification. We also examine the interesting case of reduced rings: in this case we completely classify the possible finite abelian groups of units. Our proofs are self-contained and include all the previous results for finite abelian groups of units." @default.
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- W2467176698 date "2016-07-04" @default.
- W2467176698 modified "2023-09-27" @default.
- W2467176698 title "Finite abelian groups that are the group of units of a ring" @default.
- W2467176698 hasPublicationYear "2016" @default.
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