On Weakly Separable Polynomials in Skew Polynomial Rings

TL;DR

This paper characterizes weakly separable polynomials in skew polynomial rings and explores their relation to separability, extending the concept of separable extensions in non-commutative algebra.

Contribution

It provides a new characterization of weakly separable polynomials and clarifies their relationship with separability in skew polynomial rings of derivation type.

Findings

Characterization of weakly separable polynomials in skew polynomial rings

Relation established between separability and weak separability

Extension of separable extension concepts to non-commutative rings

Abstract

The notion of weakly separable extensions was introduced by N. Hamaguchi and A. Nakajima as a generalization of separable extensions. The purpose of this article is to give a characterization of weakly separable polynomials in skew polynomial rings. Moreover, we shall show the relation between separability and weak separability in skew polynomial rings of derivation type.