A simple characterization of principal ideal domains
Volume 64 / 1993
Acta Arithmetica 64 (1993), 125-128
DOI: 10.4064/aa-64-2-125-128
Abstract
1. Introduction. In this note we give necessary and sufficient conditions for an integral domain to be a principal ideal domain. Curiously, these conditions are similar to those that characterize Euclidean domains. In Section 2 we establish notation, discuss related results and prove our theorem. Finally, in Section 3 we give two nontrivial applications to real quadratic number fields.
