Discriminant equations are an important class of Diophantine equations with close ties to
algebraic number theory, Diophantine approximation and Diophantine geometry. This book …

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 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 D be a commutative domain with field of fractions K, let A be a torsion-free D-algebra,
and let B be the extension of A to a K-algebra. The set of integer-valued polynomials on A is …

Let 𝐷 be an integral domain with quotient field 𝐾 and Ω a finite subset of 𝐷. McQuillan
proved that the ring Int (Ω, 𝐷) of polynomials in 𝐾 [𝑋] which are integervalued over Ω, that is …

In this article, we compile the work done by various mathematicians on the topic of the fixed
divisor of a polynomial. This article explains most of the results concisely and is intended to …

Let $ S $ be a subset of $\overline {\mathbb Z} $, the ring of all algebraic integers. A
polynomial $ f\in\mathbb Q [X] $ is said to be integral-valued on $ S $ if $ f (s)\in\overline …