ArticleOriginal scientific text
Title
A simple characterization of principal ideal domains
Authors 1
Affiliations
- Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania. 18015, U.S.A.
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.
Bibliography
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Pages:
125-128
Main language of publication
English
Received
1991-12-18
Accepted
1992-11-20
Published
1993
Exact and natural sciences