Properties of Armendariz rings and weak Armendariz rings. (English) Zbl 1234.16016

Jokanović, Dušan

Publ. Inst. Math., Nouv. Sér. 85(99), 131-137 (2009).

Summary: We consider some properties of Armendariz and rigid rings. We prove that the direct product of rigid (weak rigid), weak Armendariz rings is a rigid (weak rigid), weak Armendariz ring. On the assumption that the factor ring \(R/I\) is weak Armendariz, where \(I\) is nilpotent ideal, we prove that \(R\) is a weak Armendariz ring. We also prove that every ring isomorphism preserves weak skew Armendariz structure. Armendariz rings of Laurent power series are also considered.

MSC:

16S36	Ordinary and skew polynomial rings and semigroup rings
16U80	Generalizations of commutativity (associative rings and algebras)
16N40	Nil and nilpotent radicals, sets, ideals, associative rings
16W20	Automorphisms and endomorphisms

Keywords:

rigid rings; direct products; weak Armendariz rings; nilpotent ideals; weak skew Armendariz rings