Integer-valued Polynomials on Algebras
نویسنده
چکیده
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). 2000 MSC: Primary 13F20; Secondary 16S50, 13B25, 13J10, 11C08, 11C20.
منابع مشابه
Integer-valued Polynomials on Algebras a Survey
We compare several different concepts of integer-valued polynomials on algebras and collect the few results and many open questions to be found in the literature. (2000 Math. Subj. Classification: Primary 13F20; Secondary 16S50, 13B25, 13J10, 11C08, 11C20)
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