On the structure of semi-invariant polynomials in Ore extensions

JOURNAL OF ALGEBRA

卷:322

Article

Chuang, Chen-Lian²  Tsai, Yuan-Tsung¹ 

[1] Tatung Univ, Dept Appl Math, Taipei 104, Taiwan

[2] Natl Taiwan Univ, Dept Math, Taipei 106, Taiwan

关键词: Skew derivations;    Ore extensions;    Skew polynomials;    Semi-invariant polynomials;    Cv-polynomials;   

DOI  :  10.1016/j.jalgebra.2009.06.022

来源: Elsevier

【 摘 要 】

Let D be an X-outer S-derivation of a prime ring R, where S is an automorphism of R. The following is proved among other things: The degree of the minimal semi-invariant polynomial of the Ore extension R[X; S, D] is. if char R = 0, and is p(k)nu for some k >= 0 if char R = p >= 2, where nu is the least integer nu >= 1 such that S-nu DS-nu - D is X-inner. A similar result holds for cv-polynomials. These are done by introducing the new notion of k-basic polynomials for each integer k >= 0, which enable us to analyze semi-invariant polynomials inductively. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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