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Factorial domains
Author(s):
Clifford
S.
Queen
Journal:
Proc. Amer. Math. Soc.
124
(1996),
11-16.
MSC (1991):
Primary 13M15
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Abstract:
We give a simple characterization of factorial domains. We also characterize almost factorial domains and Krull domains with finite cyclic class group.
References:
- 1
- Harvey Cohn, Advanced number theory, Dover, 1980.MR 82b:12001
- 2
- R. M. Fossum, The divisor class group of a Krull domain, Ergeb. Math. Grenzgeb. (3), bd. 74, Springer, Berlin, 1973. MR 52:3139
- 3
- A. Fröhlich and M. J. Taylor, Algebraic number theory, Cambridge Univ. Press, Cambridge, No. 27, 1993. CMP 93 11
- 4
- Helmut Hasse, Über eindeutige Zerlegung in Primelemente order in Primehuapideale in Integritatsbereichen J. Reine Angew. Math. 159 (1928).
- 5
- Gerald J. Janusz, Algebraic number fields, Academic Press, New York, 1973.MR 51:3110
- 6
- Nathan Jacobson, Basic algebra I, second ed., Freeman, New York, 1985.MR 86d:00001
- 7
- C. S. Queen, Euclidean like characterizations of Dedekind, Krull and factorial domains, J. Number Theory 47 (1994). MR 95f:13025
- 8
- G. Rabinowitsch, Eindeutigkeit der Zerlegung in Primzahlfaktoren in quadrat ischen Zahlkörpern, J. Reine Angew. Math 142 (1913), 153--164.
- 9
- P. Samuel, Lectures on unique factorization domains, Tata Institute of Fundamental Research, Bombay, 1964.MR 35:5428
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Additional Information:
Clifford
S.
Queen
Affiliation:
Department of Mathematics, Christmas-Saucon Hall, Lehigh University, 14 E. Packer Avenue, Bethlehem, Pennsylvania 18015
Email:
csq0@lehigh.edu
DOI:
10.1090/S0002-9939-96-02969-3
PII:
S 0002-9939(96)02969-3
Received by editor(s):
February 18, 1994
Received by editor(s) in revised form:
June 4, 1994
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
1996,
American Mathematical Society
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