Two questions of L. Va${\rm \check{\textbf{s}}}$ on *-clean rings
Rings and Algebras
2011-07-07 v1
Abstract
A ring with an involution * is called (strongly) *-clean if every element of is the sum of a unit and a projection (that commute). All *-clean rings are clean. Va [L. Va, *-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 both questions by several examples. Moreover, some characterizations of unit regular and *-regular rings are provided.
Cite
@article{arxiv.1107.1068,
title = {Two questions of L. Va${\rm \check{\textbf{s}}}$ on *-clean rings},
author = {Jianlong Chen and Jian Cui},
journal= {arXiv preprint arXiv:1107.1068},
year = {2011}
}