Some remarks on skew polynomial rings over reduced rings. (English) Zbl 1024.16016

Kim, Hong Kee

EAMJ, East Asian Math. J. 17, No. 2, 275-286 (2001).

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

Keywords:

Baer rings; right annihilators; idempotents; reduced rings; skew polynomial rings