On Almost Unit-Regular Rings |
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Authors: | Huanyin Chen |
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Institution: | 1. Department of Mathematics , Hangzhou Normal University , Hangzhou , China huanyinchen@yahoo.cn |
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Abstract: | An element a ∈ R is unit-regular provided that there exists an invertible u ∈ R such that a = aua. A ring R is called an almost unit-regular ring provided that for any a ∈ R, either a or 1 ? a is unit-regular. We characterize, in this article, the almost unit-regularity of Morita contexts with zero pairings. We also show that a ring R is unit-regular if and only if M 2(R) is almost unit-regular. Various examples of such rings are constructed by means of formal triangular matrix rings. |
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Keywords: | Almost unit-regular ring Matrix extension Morita context |
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