Integer-valued polynomials on algebras

Let D be a domain with quotient field K and A a D-algebra. A polynomial with coefficients in K that maps every element of A to an element of A is called integer-valued on A. For commutative A we also consider integer-valued polynomials in several variables. For an arbitrary domain D and I an arbitra...

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Bibliographic Details
Published in:Journal of algebra Vol. 373; pp. 414 - 425
Main Author: Frisch, Sophie
Format: Journal Article
Language:English
Published: Elsevier Inc 01.01.2013
Subjects:
I-adic topology
Integer-valued polynomials
Krull dimension
Matrix algebras
Non-commutative algebras
Non-commuting variables
Polynomial functions
Polynomial mappings
Polynomial rings
Spectrum
secondary
Krull dimension
Polynomial functions
Matrix algebras
Polynomial rings
Integer-valued polynomials
Non-commuting variables
I-adic topology
Non-commutative algebras
Polynomial mappings
primary
Spectrum
ISSN:0021-8693, 1090-266X
Online Access:Get full text
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Summary:Let D be a domain with quotient field K and A a D-algebra. A polynomial with coefficients in K that maps every element of A to an element of A is called integer-valued on A. For commutative A we also consider integer-valued polynomials in several variables. For an arbitrary domain D and I an arbitrary ideal of D we show I-adic continuity of integer-valued polynomials on A. For Noetherian one-dimensional D, we determine spectrum and Krull dimension of the ring IntD(A) of integer-valued polynomials on A. We do the same for the ring of polynomials with coefficients in Mn(K), the K-algebra of n×n matrices, that map every matrix in Mn(D) to a matrix in Mn(D).
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2012.10.003