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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Vydáno v:	Journal of algebra Ročník 373; s. 414 - 425
Hlavní autor:	Frisch, Sophie
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.01.2013
Témata:	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
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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