A simple characterization of principal ideal domains

Volume 64 / 1993

Clifford Queen Acta Arithmetica 64 (1993), 125-128 DOI: 10.4064/aa-64-2-125-128


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

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