# UU Group Rings

### Abstract

A ring is called UU if each its unit is a unipotent. We prove that the group ring R[G] is a commutative UU ring if, and only if, R is a commutative UU ring and G is an abelian 2-group. This extends a result due to McGovern-Raja-Sharp (J. Algebra Appl., 2015) established for commutative nil-clean group rings. In some special cases we also discover when R[G] is a non-commutative UU ring as our results are closely related to those obtained by Ko¸san-Wang-Zhou (J. Pure Appl. Algebra, 2016) and Sahinkaya-Tang-Zhou (J. Algebra Appl., 2017).

Published

2018-12-26

How to Cite

DANCHEV, Peter; ALMALLAH, Omar Abdelhameed.
UU Group Rings.

**Eurasian Bulletin of Mathematics (ISSN: 2687-5632)**, [S.l.], p. 94-97, dec. 2018. ISSN 2687-5632. Available at: <http://www.ebmmath.com/index.php/EBM/article/view/26>. Date accessed: 21 sep. 2020.
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