%0 Journal Article
%T Integer-valued polynomials on algebras
%A Sophie Frisch
%J Mathematics
%D 2012
%I arXiv
%R 10.1016/j.jalgebra.2012.10.003
%X Let D be a domain with quotient field K and A a D-algebra. We call a polynomial with coefficients in K that maps every element of A to an element of A "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 the spectrum and Krull dimension of the ring Int_D(A) of integer-valued polynomials on A. We do the same for the ring of polynomials with coefficients in M_n(K), the K-algebra of n x n matrices, that map every matrix in M_n(D) to a matrix in M_n(D).
%U http://arxiv.org/abs/1210.1474v3