Clear rings and clear elements - Zabavsky, B. V.; Domsha, O. V.; Romaniv, O. M. (Matematychni Studii, 2021)
An element of a ring R is called clear if it is a sum of a unit-regular element and a unit. An associative ring is clear if each of its elements is clear. In this paper we defined clear rings and extended many results to a wider class. Finally, we proved that a commutative Bezout domain is an elementary divisor ring if and only if every full 2× 2 matrix over it is nontrivially clear.