Rings with prime units

Authors

  • T.P. Calci Ankara University, Dögol str., 06100 Beşevler, Ankara, Türkiye https://orcid.org/0000-0003-0950-008X
  • H. Chen Hangzhou Normal University, 2318 Yuhangtang Rd., Hangzhou, China
  • S. Halicioglu Ankara University, Dögol str., 06100 Beşevler, Ankara, Türkiye
https://doi.org/10.15330/cmp.17.1.152-158

Keywords:

$UP$ ring, ring extension, exchange ring
Published online: 2025-06-12

Abstract

A ring $R$ is said to be a $UP$ ring if every invertible element in $R$ is the sum of the identity and a strongly nilpotent element. In this paper, many characterizations of $UP$ rings are given. We prove that for a $UP$ ring $R$, the following conditions are equivalent: $R$ is weakly exchange, $R$ is exchange, $R$ is clean, and $R$ is nil clean. This is a partial answer to the question, which is asked by A.J. Diesl in [J. Algebra 2013, 383, 197$-$211].

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How to Cite
(1)
Calci, T.; Chen, H.; Halicioglu, S. Rings With Prime Units. Carpathian Math. Publ. 2025, 17, 152-158.