A simple characterization of principal ideal domains

• Autorzy: Clifford S. Queen
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 64
• Numer: 2
• Strony: 125-128

Daty

wydano

1993

otrzymano

1991-12-18

poprawiono

1992-11-20

Twórcy

autor

Clifford S. Queen

• Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania. 18015, U.S.A.

Bibliografia

• [1] H. Cohn, Advanced Number Theory, Dover, 1980.
• [2] N. Jacobson, Basic Algebra I, 2nd ed., Freeman, 1985.
• [3] M. Kutsuna, On a criterion for the class number of a real quadratic field to be one, Nagoya Math. J. 79 (1980), 123-129.
• [4] T. Motzkin, The Euclidean algorithm, Bull. Amer. Math. Soc. 55 (1949), 1142-1146.
• [5] C. Queen, Arithmetic euclidean rings, Acta Arith. 26 (1974), 105-113.
• [6] G. Rabinowitsch, Eindeutigkeit der Zerlegung in Primzahlfaktoren in quadratischen Zahlkörpern, J. Reine Angew. Math. 142 (1913), 153-164.
• [7] P. Samuel, About Euclidean rings, J. Algebra 19 (1971), 282-301.