On extended quasi-Armendariz rings

TL;DR

This paper explores generalizations of quasi-Armendariz rings, introducing new concepts like quasi α-Armendariz and quasi α-skew Armendariz rings, and examines their properties, including in Laurent type rings.

Contribution

It extends the theory of quasi-Armendariz rings by defining and analyzing new variants such as quasi α-Armendariz and quasi α-skew Armendariz rings, and studies their properties.

Findings

Introduction of quasi α-Armendariz and quasi α-skew Armendariz rings

Analysis of properties of these rings in various contexts

Investigation of quasi Armendariz properties in Laurent type rings

Abstract

This paper deals with the quasi-Armendariz ring in general setting. We generalize the notions of quasi-Armendariz and $\alpha$-skew Armendariz ring to quasi $\alpha$-Armendariz and quasi $\alpha$-skew Armendariz ring and investigate their properties. We also consider the quasi Armendariz properties of Laurent type rings.