Nagoya Mathematical Journal

A construction of quintic rings

Anthony C. Kable and Akihiko Yukie

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We construct a discriminant-preserving map from the set of orbits in the space of quadruples of quinary alternating forms over the integers to the set of isomorphism classes of quintic rings. This map may be regarded as an analogue of the famous map from the set of equivalence classes of integral binary cubic forms to the set of isomorphism classes of cubic rings and may be expected to have similar applications. We show that the ring of integers of every quintic number field lies in the image of the map. These results have been used to establish an upper bound on the number of quintic number fields with bounded discriminant.

Article information

Nagoya Math. J., Volume 173 (2004), 163-203.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11R21: Other number fields
Secondary: 11E76: Forms of degree higher than two 11R27: Units and factorization 11S90: Prehomogeneous vector spaces


Kable, Anthony C.; Yukie, Akihiko. A construction of quintic rings. Nagoya Math. J. 173 (2004), 163--203.

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