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arXiv · 2001.01058

Finite unitary rings with a single subgroup of prime order of the group of units

Mostafa Amini·Mohsen Amiri
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Abstract

Let R be a unitary ring of finite cardinality P^k, where p is a prime number and $p\nmid k$. We show that if the group of units of $R$ has at most one subgroup of order $p$, then $R\cong A\bigoplus B,$ where $B$ is a finite ring of order $k$ and $A$ is a ring of cardinality $p^{\beta}$ which is one of the six explicitly described types.

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Mostafa Amini, Mohsen Amiri. 2020-01-04. Finite unitary rings with a single subgroup of prime order of the group of units. https://arxiv.org/abs/2001.01058

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