On matrix rings over unit-regular rings.
Lok, Tsan-Ming, Shum, K.P. (2003)
Beiträge zur Algebra und Geometrie
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Lok, Tsan-Ming, Shum, K.P. (2003)
Beiträge zur Algebra und Geometrie
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Huanyin Chen, Fu-An Li (2002)
Collectanea Mathematica
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In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.
O. Marrero (1979)
Revista Matemática Hispanoamericana
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Ehrlich, Gertrude (1968)
Portugaliae mathematica
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Pere Ara, Kenneth R. Goodearl (1992)
Publicacions Matemàtiques
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A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been done by P. Menal, K. C. O'Meara, and the authors. To clarify some aspects of these new developments, we introduce and study the notion of almost isomorphism between finitely generated projective modules over a simple regular ring.
Agayev, Nazim, Güngöroğlu, Gonca, Harmanci, Abdullah, Halicioğlu, S. (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Huanyin Chen (2008)
Czechoslovak Mathematical Journal
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Let be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.
Roger Yue Chi Ming (1981)
Rendiconti del Seminario Matematico della Università di Padova
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Raphael, R. (1999)
Theory and Applications of Categories [electronic only]
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