ONE-SIDED UNIT-REGULAR IDEALS OF REGULAR RINGS

Huanyin Chen

doi:10.11650/twjm/1500407717

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Home > Journals > Taiwanese J. Math. > Volume 8 > Issue 4 > Article

2004 ONE-SIDED UNIT-REGULAR IDEALS OF REGULAR RINGS

Huanyin Chen

Taiwanese J. Math. 8(4): 761-770 (2004). DOI: 10.11650/twjm/1500407717

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Abstract

In this paper, we investigate one-sided unit-regular ideals of regular rings. Let $I$ be a purely infinite, simple and essential ideal of a regular ring $R$. It is shown that $R$ is one-sided unit-regular if and only if so is $R/I$. Also we prove that every square matrix over one-sided unit-regular ideals of regular rings admits a diagonal matrix with idempotent entries.