Polynomial functions on upper triangular matrix algebras |
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Authors: | Email author" target="_blank">Sophie?FrischEmail author |
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Institution: | 1.Institut für Mathematik A,Technische Universit?t Graz,Graz,Austria |
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Abstract: | There are two kinds of polynomial functions on matrix algebras over commutative rings: those induced by polynomials with coefficients in the algebra itself and those induced by polynomials with scalar coefficients. In the case of algebras of upper triangular matrices over a commutative ring, we characterize the former in terms of the latter (which are easier to handle because of substitution homomorphism). We conclude that the set of integer-valued polynomials with matrix coefficients on an algebra of upper triangular matrices is a ring, and that the set of null-polynomials with matrix coefficients on an algebra of upper triangular matrices is an ideal. |
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