Elementary divisors, Hochster duality, and spectra

Abstract

It is proved that every Bézout domain admits an embedding into an elementary divisor domain with the same divisibility group. So the prime spectrum of a Bézout domain is homeomorphic to the prime spectrum of an elementary divisor domain. Together with an earlier result, it follows that a topological space is homeomorphic to the maximal spectrum of an elementary divisor domain if and only if it is a serial quasi-compact \(T_1\)-space.