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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