zbMATH — the first resource for mathematics

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)
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