Ore Extensions of Skew Armendariz Rings

Abstract

Let α be an endomorphism and δ an α-derivation of a ring R. We introduce the notion of skew-Armendariz rings which are a generalization of α-skew Armendariz rings and α-rigid rings and extend the classes of non reduced skew-Armendariz rings. Some properties of this generalization are established, and connections of properties of a skew-Armendariz ring R with those of the Ore extension R[x; α, δ] are investigated. As a consequence we extend and unify several known results related to Armendariz rings.

Key Words:

• Baer ring
• Quasi-Baer ring
• Skew-Armendariz ring
• Skew polynomial ring

2000 Mathematics Subject Classification:

• 16S36

Notes

Communicated by V. A. Artamonov.