Abstract
In this paper we introduce full elements in regular rings, and show that every matrix over regular rings admits a diagonal reduction by full matrices. Also we get that a regular ring $R$ is unit-regular if and only if $aR\cong bR$ with full elements $a,b\in R$ implies $a=ubv$ for some units $u,v\in R$.
Citation
Huanyin Chen. "FULL ELEMENTS IN REGULAR RINGS." Taiwanese J. Math. 8 (2) 203 - 209, 2004. https://doi.org/10.11650/twjm/1500407622
Information