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 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 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). (C) 2012 Elsevier Inc. All rights reserved.