FULL ELEMENTS IN REGULAR RINGS

Huanyin Chen

doi:10.11650/twjm/1500407622

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Home > Journals > Taiwanese J. Math. > Volume 8 > Issue 2 > Article

2004 FULL ELEMENTS IN REGULAR RINGS

Huanyin Chen

Taiwanese J. Math. 8(2): 203-209 (2004). DOI: 10.11650/twjm/1500407622

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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 $u,v\in R$.