Two questions of L. Vas on *-clean rings

Authors

  • J. Chen Southeast University
  • J. Cui Anhui Normal University

Keywords:

$*$-clean ring, strongly $*$-clean ring, $*$-regular ring, strongly clean ring, unit regular ring

Abstract

A $*$-ring $R$ is called (strongly) $*$-clean if every element of $R$ is the sum of a unit and a projection (that commute). Vas [L. Vas, $*$-Clean rings; some clean and almost clean Baer $*$-rings and von Neumann algebras, J. Algebra 324(12) (2010), 3388-3400] asked whether there exists a $*$-ring that is clean but not $*$-clean and whether a unit regular and $*$-regular ring is strongly $*$-clean. In this paper, we answer the two questions. Moreover, some characterizations related to $*$-regular rings are given. 10.1017/S0004972713000117

Author Biographies

J. Chen, Southeast University

Department of Mathematics

J. Cui, Anhui Normal University

Department of Mathematics

Published

2013-09-27

Issue

Vol. 88 No. 3 (2013)

Section

Articles
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