On the structure of semi-invariant polynomials in Ore extensions
Resource
Journal of Algebra 322 (7): 2464-2491
Journal
Journal of Algebra
Pages
2464-2491
Date Issued
2009
Date
2009
Author(s)
Chuang, C.L.
Tsai, Y.T.
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 R [X ; S, D] is ν if char R = 0, and is pk ν for some k ≥ 0 if char R = p ≥ 2, where ν is the least integer ν ≥ 1 such that Sν D S- 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 k ≥ 0, which enable us to analyze semi-invariant polynomials inductively. © 2009 Elsevier Inc. All rights reserved.
Type
journal article
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