## Nagoya Mathematical Journal

### A construction of quintic rings

#### Abstract

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

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

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114631987

Mathematical Reviews number (MathSciNet)
MR2041760

Zentralblatt MATH identifier
1068.11068

#### Citation

Kable, Anthony C.; Yukie, Akihiko. A construction of quintic rings. Nagoya Math. J. 173 (2004), 163--203. https://projecteuclid.org/euclid.nmj/1114631987

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