Sums and products of units and idempotents in duo rings

Abstract

An element in a ring R is said to be clean (respectively unit-regular) if it is a sum (respectively product) of an invertible element and an idempotent. It is known that all elements in R are clean, if all of them are unit-regular. We study some classes of unit-regular and clean matrices over a duo ring. It is shown that a right adequate duo domain is almost 2-good ring. Cite as: A. I. Gatalevych, M. I. Kuchma, Non-singular solutions of one class of matrix equations over a polynomial ring, Prykl. Probl. Mekh. Mat. , Issue 17, 42–46 (2019) (in Ukrainian), https://doi.org/10.15407/apmm2019.17.42-46