IMI/Publicaţii/BASM/Ediţii/BASM n.2 (8), 1992/

Regular and strongly regular rings with respect to a right ideal. (Russian)

Authors: Andrunakievich A. V., Andrunakievich V. A.


The right ideal $P$ of the ring $R$ we call strictly reduced, if for any right ideal $Q\supseteq P$ the relation $a^2\in Q\Rightarrow a\in Q$ takes place. It is proved that the regular ring relative to the right ideal $P(axa-a\in P, ax\in P)$, where $a,x\in P$, is strictly regular relative to the same $P(a^2x-a\in P, ax\in P)$ if and only if $P$ is strictly reduced right ideal.