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Some remarks on skew polynomial rings over reduced rings. (English) Zbl 1024.16016
A ring $$R$$ is called Baer if the right annihilator of every nonempty subset of $$R$$ is generated, as a right ideal, by an idempotent of $$R$$. For a reduced ring $$R$$ and a monomorphism $$\alpha$$ of $$R$$ with $$\alpha(P)\subseteq P$$ for any minimal prime ideal $$P$$ of $$R$$, it is shown that the skew polynomial ring $$R[x;\alpha]$$ is Baer if and only if $$R$$ is Baer.
Reviewer: J.K.Park (Pusan)
##### MSC:
 16S36 Ordinary and skew polynomial rings and semigroup rings 16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras) 16D10 General module theory in associative algebras 16D25 Ideals in associative algebras