Geodesic
A simple characterization of principal ideal domains
Acta Arithmetica, Tome 64 (1993) no. 2, pp. 125-128

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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. 
Clifford Queen. A simple characterization of principal ideal domains. Acta Arithmetica, Tome 64 (1993) no. 2, pp. 125-128. doi: 10.4064/aa-64-2-125-128
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