Quasi-Duo Skew Polynomial Rings

TL;DR

This paper characterizes when skew polynomial and Laurent polynomial rings are quasi-duo, revealing conditions under which right and left quasi-duo properties coincide, and extends known results in ring theory.

Contribution

It provides new characterizations of quasi-duo skew polynomial rings and answers a question about the symmetry of right and left quasi-duo properties.

Findings

Polynomial ring R[x] is right quasi-duo iff R[x] is commutative modulo its Jacobson radical.

Skew Laurent polynomial ring is right quasi-duo iff it is left quasi-duo.

Extends known results and partially answers Lam and Dugas' question.

Abstract

A characterization of right (left) quasi-duo skew polynomial rings of endomorphism type and skew Laurent polynomial rings are given. In particular, it is shown that (1) the polynomial ring R[x] is right quasi-duo iff R[x] is commutative modulo its Jacobson radical iff R[x] is left quasi-duo, (2) the skew Laurent polynomial ring is right quasi-duo iff it is left quasi-duo. These extend some known results concerning a description of quasi-duo polynomial rings and give a partial answer to the question posed by Lam and Dugas whether right quasi-duo rings are left quasi-duo.