Irreducible skew polynomials over domains

Abstract

Let $S$ be a domain and $R=S[t;\sigma,\delta]$ a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$ -derivation. We give criteria for skew polynomials $f\in R$ of degree less or equal to four to be irreducible. We apply them to low degree polynomials in quantized Weyl algebras and the quantum planes. We also consider $f(t)=t^m-a\in R$.