Integer-valued polynomials on algebras - Frisch, Sophie (Journal of algebra, 2013)
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).