On Weakly Separable Polynomials in Skew Polynomial 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.

15 pages. Author's accepted manuscript of the article published in Math. J. Okayama Univ. 64 (2022), 47-61