IMI/Publicaţii/BASM/Ediţii/BASM n.2 (15), 1994/

On the property of a right ideal of a ring to be two-sided. (Russian)

Authors: Andrunakievich A. V.


The assiciative ring $R$ not obligatory with a unity is considered. Let $P\triangleleft R_R$ a fully reduced right ideal, i.e. $a^2Q\Longrightarrow a\in Q$, where $a\in R$, $Q\triangleleft R_R$, $Q\supseteq P$. If for any $r\in R$ there is $P$-idempotent $e\in R$, i.e. $e\notin P$, $e^2 e\in P$, $eP\subseteq P$ and for $Q\triangleleft R_R$, $Q\supseteq P$ implication takes place, $e\notin Q\Longrightarrow r\in Q$, $P$ is proved to be a two - sided ideal.

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