Reduced Archimedean skew polynomial rings and skew power series rings

TL;DR

This paper characterizes when skew polynomial and skew power series rings are reduced and Archimedean on either side, providing a clearer understanding of their algebraic structure.

Contribution

It offers a characterization of reduced and Archimedean properties in skew polynomial and skew power series rings, which was previously not well-understood.

Findings

Identifies conditions for skew polynomial rings to be reduced and Archimedean.

Provides criteria for skew power series rings to have these properties.

Enhances understanding of the structure of skew rings in algebra.

Abstract

We characterize skew polynomial rings and skew power series rings that are reduced and right or left Archimedean.