@article{Zabavsky_Domsha_Romaniv_2021, title={Clear rings and clear elements}, volume={55}, url={http://matstud.org.ua/ojs/index.php/matstud/article/view/126}, DOI={10.30970/ms.55.1.3-9}, abstractNote={<p>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.<br>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 $2\times 2$ matrix over it is nontrivially clear.</p>}, number={1}, journal={Matematychni Studii}, author={Zabavsky, B. V. and Domsha, O. V. and Romaniv, O. M.}, year={2021}, month={Mar.}, pages={3-9} }