Polynomial functions on upper triangular matrix algebras

作     者：Frisch, Sophie 

作者机构：Graz Univ Technol Inst Math Kopernikusgasse 24 A-8010 Graz Austria 

出 版 物：《MONATSHEFTE FUR MATHEMATIK》 (数学月刊)

年 卷 期：2017年第184卷第2期

页      面：201-215页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Graz University of Technology 

主　　题：Integer-valued polynomials Null polynomials Zero polynomials Polynomial functions Upper triangular matrices Matrix algebras Polynomials on non-commutative algebras Matrices over commutative rings 

摘      要：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.