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On reduced right ideals of a ring. (English)

Authors: Andrunakievich V. A., Reabuhin Iuri

Abstract

In the work we study reduced right ideals $P$ of a ring $R$ (i.e. $r^2\in P\Rightarrow r\in P$). It is demonstrate that if $P$ is a strongly reduced ideal (i.e. ewery right ideal $T\supseteq P$ is reduced), then $P$ is a bilateral ideal of $R$ and $R/P$ is a strongly (or abelian) regular ring. As the corollary we obtain a criterion of the decomposition of a ring $R$ to the subdirect product of division rings.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău MD-2028, Moldova