This chapter consists of a collection of open problems in commutative algebra. The
collection covers a wide range of topics from both Noetherian and non-Noetherian ring …

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 …

There are two kinds of polynomial functions on matrix algebras over commutative rings:
those induced by polynomials with coefficients in the algebra itself and those induced by …

Let D be a commutative domain with field of fractions K and let A be a torsion-free D-algebra
such that A ∩ K= DA∩ K= D. The ring of integer-valued polynomials on A with coefficients in …

Let D be a domain with fraction field K, and let M n (D) be the ring of n× n matrices with
entries in D. The ring of integer-valued polynomials on the matrix ring M n (D), denoted Int K …

Given a commutative integral domain D with fraction field K, the ring of integer-valued
polynomials on D is Int (D)={f∈ K [x]∣ f (D)⊆ D}. In recent years, attention has turned to …

Let M n (Z) denote the ring of n× n matrices with integer entries and Int Q (M n (Z))⊆ Q [x] the
algebra of polynomials that preserve M n (Z), ie polynomials for which f (M)∈ M n (Z) if M∈ …

Let DD be an integrally closed domain with quotient field KK and n na positive integer. We
give a characterization of the polynomials in KXKX which are integer-valued over the set of …

Let D be an integrally closed domain with quotient field K. Let A be a torsion-free D-algebra
that is finitely generated as a D-module. For every a in A we consider its minimal polynomial …

Let K be a number field of degree n with ring of integers O K. By means of a criterion of
Gilmer for polynomially dense subsets of the ring of integers of a number field, we show that …