TY - JOUR
AU - Zabavsky, B. V.
AU - Domsha, O. V.
AU - Romaniv, O. M.
PY - 2021/03/03
Y2 - 2021/12/08
TI - Clear rings and clear elements
JF - Matematychni Studii
JA - Mat. Stud.
VL - 55
IS - 1
SE - Articles
DO - 10.30970/ms.55.1.3-9
UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/126
SP - 3-9
AB - 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 $2\times 2$ matrix over it is nontrivially clear.
ER -