X-inner automorphisms, automorphisms, and isomorphisms of skew polynomial rings

摘要

In this paper, we examine the X-inner automorphisms, automorphisms, and isomorphisms of skew polynomial rings of the form K[x][y;delta], where K is a field of characteristic 0 and delta is a derivation of K[x] such that x(delta) is a polynomial of degree greater than or equal to 1. We (1) determine the group of X-inner automorphisms of K[x][y;delta], (2) analyze the structure of the group of automorphisms of K[x][y;delta], and (3) examine the isomorphism classes of skew polynomial rings of the form K[x][y;delta]. We also provide several examples which indicate the importance of the base field in computing the X-inner automorphisms, automorphisms, and isomorphism classes of K[x][y;delta]. [References: 3]