On the structure of semi-invariant polynomials in Ore extensions |
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Authors: | Chen-Lian Chuang Yuan-Tsung Tsai |
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Institution: | aDepartment of Mathematics, National Taiwan University, Taipei 106, Taiwan;bDepartment of Applied Mathematics, Tatung University, Taipei 104, Taiwan |
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Abstract: | 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 RX;S,D] is ν if charR=0, and is pkν for some k0 if charR=p2, where ν is the least integer ν1 such that SνDS−ν−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 k0, which enable us to analyze semi-invariant polynomials inductively. |
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Keywords: | Skew derivations Ore extensions Skew polynomials Semi-invariant polynomials Cv-polynomials |
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