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arXiv · 1605.06027

Polynomial functions on upper triangular matrix algebras

Sophie Frisch
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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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Sophie Frisch. 2016-10-26. Polynomial functions on upper triangular matrix algebras. https://arxiv.org/abs/1605.06027

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