On weakly $(tilde{rho}, tilde{D})$-separable polynomials in skew polynomial rings (Algebras, logics, languages and related areas)

Abstract

Separable polynomials in skew polynomial rings were studied extensively by Y. Miyashita, T. Nagahara, S. Ikehata, and G. S eto. In particular, Ikehata gave the characteri ation of (overline{rho}, overline{D})-separable polynomials in skew polynomial rings. In this article, we shall introduce the notion of weakly (overline{rho}, tilde{D})-separable polynomials in skew polynomial rings, and we shall give a characteri ation of the (overline{p}, overline{D})-separability and that of the weak (overline{rho}, overline{D})-separability.