Commuting polynomials and λ-ring structures on Z[x]
نویسندگان
چکیده
منابع مشابه
Commuting polynomials and self-similarity
Let F be an algebraically closed field of characteristic 0 and f(x) a polynomial of degree strictly greater than one in F [x]. We show that the number of degree k polynomials with coefficients in F that commute with f (under composition) is either zero or equal to the number of degree one polynomials with coefficients in F that commute with f . As a corollary, we obtain a theorem of E. A. Bertr...
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Let X = (xij) and Y = (yij) be generic n by n matrices and Z = XY − Y X. Let S = k[x11, . . . , xnn, y11, . . . , ynn], where k is a field, let I be the ideal generated by the entries of Z and let R = S/I . We give a conjecture on the first syzygies of I , show how these can be used to give a conjecture on the canonical module of R. Using this and the Hilbert series of I we give a conjecture on...
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The multivariate orthogonal polynomials are related to a family of operators whose matrix representations are block Jacobi matrices. A sufficient condition is given so that these operators, in general unbounded, are commuting and selfadjoint. The spectral theorem for these operators is used to establish the existence of the measure of orthogonality in Favard's theorem.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1994
ISSN: 0022-4049
DOI: 10.1016/0022-4049(94)90061-2