Sophie Frisch

Integer-valued polynomials on algebras

Abstract 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 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 × n matrices, that map every matrix in M n ( D ) to a matrix in M n ( D ) .

A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite non-empty set

Non-unique factorization of polynomials over residue class rings of the integers

S

Finitely additive measures on groups and rings

of natural numbers greater

Polynomial functions on upper triangular matrix algebras

1

Integer-valued polynomials on Krull rings

, we construct