Chen, Huanyin On partially unit-regularity. (English) Zbl 1008.16009 Kyungpook Math. J. 42, No. 1, 13-19 (2002). Summary: We investigate partially unit-regularity. We show that \(R\) is partially unit-regular if and only if whenever \(ab\) and \(ba\) are strongly \(\pi\)-regular, there exists a \(u\in U(R)\) such that \((ab)^d=u(ba)^du^{-1}\). Furthermore, we show that if \(T\) is the ring of a Morita context \((A,B,M,N,\psi,\phi)\) with zero pairings, then \(T\) is partially unit-regular if and only if so are \(A\) and \(B\). Cited in 3 Documents MSC: 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 16D90 Module categories in associative algebras 16S50 Endomorphism rings; matrix rings Keywords:partially unit-regular rings; strongly \(\pi\)-regular rings; Morita contexts PDFBibTeX XMLCite \textit{H. Chen}, Kyungpook Math. J. 42, No. 1, 13--19 (2002; Zbl 1008.16009)