Displaying similar documents to “Unit-regular rings”

Exchange rings in which all regular elements are one-sided unit-regular

Huanyin Chen (2008)

Czechoslovak Mathematical Journal

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Let R be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in R is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.

The almost isomorphism relation for simple regular rings.

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.

Adjoint regular rings.

Heatherly, Henry E., Tucci, Ralph P. (2002)

International Journal of Mathematics and Mathematical Sciences

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A Survey of Rings Generated by Units

Ashish K. Srivastava (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This article presents a brief survey of the work done on rings generated by their units.

Exchange rings satisfying the related comparability.

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.