Locally adequate duo rings as a generalization case of right adequate rings

Abstract

A locally right adequate duo-rings have been investigated, the relation between right adequate elements and neat elements in the duo Bezout domain has been shown. It has been proved that the Bezout duo domain is locally right adequate if and only if for any a,b∈R such that aR+bR=R , one of these elements is right adequate. Cite as: A. A. Dmytruk, "Locally adequate duo rings as a generalization case of right adequate rings," Prykl. Probl. Mekh. Mat. , Issue 16, 39–42 (2018) (in Ukrainian), https://doi.org/10.15407/apmm2018.16.39-42