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RELATIONS IN THE 2-CLASS GROUP OF QUADRATIC NUMBER FIELDS

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  07 February 2013

F. LEMMERMEYER
F. LEMMERMEYER*
Affiliation:
Mörikeweg 1, 73489 Jagstzell, Germany email hb3@ix.urz.uni-heidelberg.de
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Abstract

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We construct a family of ideals representing ideal classes of order two in quadratic number fields and show that relations between their ideal classes are governed by certain cyclic quartic extensions of the rationals.

Keywords

quadratic number fieldideal class groupgenus theory

MSC classification

Secondary: 11R11: Quadratic extensions 11R29: Class numbers, class groups, discriminants

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 1-2 , October 2012 , pp. 115 - 120
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc.

References

Hecke, E., Lectures on the Theory of Algebraic Numbers (Springer, New York, 1981).CrossRefGoogle Scholar
Washington, L., Introduction to Cyclotomic Fields (Springer, New York, 1982).CrossRefGoogle Scholar