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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Relative imaginary quadratic fields of class number $ 1$ or $ 2$


Author: Larry Joel Goldstein
Journal: Trans. Amer. Math. Soc. 165 (1972), 353-364
MSC: Primary 12A25
MathSciNet review: 0291124
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Abstract: Let K be a normal totally real algebraic number field. It is shown how to effectively classify all totally imaginary quadratic extensions of class number 1. Let K be a real quadratic field of class number 1, whose fundamental unit has norm $ - 1$. Then it is shown how to effectively classify all totally imaginary quadratic extensions of class number 2.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0291124-8
PII: S 0002-9947(1972)0291124-8
Keywords: Number field, class number, quadratic field
Article copyright: © Copyright 1972 American Mathematical Society