Comm. Algebra 32(5) (2004) 2015-2017
# Integrally closed domains, minimal polynomials, and
null ideals of matrices

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 J. Brewer and
F. 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 (consisting of all polynomials f in D[x] with
f(A)=0) is a principal ideal of D[x].
2000 Mathematics Subject Classification: Primary 13B22, 15A21;
Secondary 13B25, 12E05, 11C08, 11C20

PDF: Integrally closed domains, minimal polynomials, and null ideals of matrices

DVI: Integrally closed domains, minimal polynomials, ... (dvi file)

PS: Integrally closed domains, minimal polynomials, ... (PostScript)