Abstract
We show that every element of the integral closure D′ of a domain D occurs as a coefficient of the minimal polynomial of a matrix with entries in D. This answers affirmatively a question of Brewer and Richman, namely, if integrally closed domains are characterized by the property that the minimal polynomial of every square matrix with entries in D is in D[x]. It follows that a domain D is integrally closed if and only if for every matrix A with entries in D the null ideal of A, N D (A) = {f ∈ D[x] ∣ f(A) = 0} is a principal ideal of D[x].
2000 Mathematics Subject Classification:
Acknowledgments
Notes
#Communicated by A. Prestel.