X-Inner Automorphisms,Automorphisms, and Isomorphisms of Skew Polynomial Rings |
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Abstract: | Abstract In this paper, we examine the X-inner automorphisms, automorphisms, and isomorphisms of skew polynomial rings of the form K[x][y;δ], where K is a field of characteristic 0 and δ is a derivation of K [x] such that x δ is a polynomial of degree ≥ 1. We 1. determine the group of X-inner automorphisms of K [x][ y;δ], 2. analyze the structure of the group of automorphisms of K [x][ y;δ], and 3. examine the isomorphism classes of skew polynomial rings of the form K [x][ y;δ]. 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;δ]. |
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Keywords: | Skew polynomial ring Automorphism Isomorphism classes X-inner automorphism |
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