X-Inner Automorphisms,Automorphisms, and Isomorphisms of Skew Polynomial Rings

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].     

体上可中心化矩阵的几个定理

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The Matrix Equation A_(mn)X_(ns)B_(st)=Cover an Arbitrary Skew Field

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＴｈｅｃｏｎｓｉｄｅｒａｂｌｅｐｒｏｇｒｅｓｓｅｓｈａｖｅｂｅｅｎｍａｄｅｉｎｔｈｅｔｈｅｏｒｙｏｆｍａｔｒｉｃｅｓｏｖｅｒｓｋｅｗｆｉｅｌｄｓｓｉｎｃｅｐｒｏｆｅｓｓｏｒＸｉｅＢａｎｄｊｉｅｓｉｍｐｏｒｔａｎｔｐａｐｅｒ［１］ｗａｓｐｕｂｌｉｓｈｅｄ．Ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔｍａｔｒｉｘｅｑｕａｔｉｏｎｉｓｏｎｅｏｆｉｍｐｏｒｔａｎｔｃｏｎｔｅｎｔｓｏｆｍａｔｒｉｘｓｔｕｄｙ．Ｉｎ［２－４］，ｆｉｖｅｔｙｐｅｓｏｆｍａ…     

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ＯｎａＳｙｓｔｅｍｏｆＭａｒｔｉｘＥｑｕａｔｉｏｎｓｏｖｅｒａｎＡｒｂｉｔｒａｒｙＳｋｅｗＦｉｅｌｄ￥ＷａｎｇＱｉｎｇｗｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＣｈａｎｇｗｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｙｅ，Ｗｅｉｆａｎｇ，Ｗｅｉｆａｎｇ，２６１０４３）Ａｂ...     

任意除环上一矩阵方程组的一般解与中心和反中心对称解

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Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two

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A Further Study of the System of Matrix Equations over a Skew Field

,ＡＦｕｒｔｈｅｒＳｔｕｄｙｏｆｔｈｅＳｙｓｔｅｍｏｆＭａｔｒｉｘＥｑｕａｔｉｏｎｓｏｖｅｒａＳｋｅｗＦｉｅｌｄ￥ＷａｎｇＱｉｎｇｗｅｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＣｈａｎｇｗｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，Ｗｅｉｆａｎｇ，２６１０４３）Ｗａｎｇ?..     

任意体上的双矩阵分解与矩阵方程

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Automorphisms of (B)-geometries

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体上代数矩阵的素有理标准形与特征值

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Classical Integrable Systems and Automorphisms of Representations of gl(2)

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