Skip to main content
Log in

A Ring of Pythagorean Triples over Quadratic Fields

  • Published:
Ukrainian Mathematical Journal Aims and scope

Let K be a quadratic field and let R be the ring of integers of K such that R is a unique factorization domain. The set P of all Pythagorean triples in R is partitioned into P η , sets of triples 〈αβγ〉 in P where η = γ − β. We show the ring structures of each P η and P from the ring structure of R.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. B. Dawson, “A ring of Pythagorean triples,” Missouri J. Math. Sci., 6, 72–77 (1994).

    MATH  MathSciNet  Google Scholar 

  2. J. T. Cross, “Primitive Pythagorean triples of Gaussian integers,” Math. Mag., 59, No. 2, 106–110 (1986).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 1, pp. 135–139, January, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Somboonkulavudi, C., Harnchoowong, A. A Ring of Pythagorean Triples over Quadratic Fields. Ukr Math J 66, 153–159 (2014). https://doi.org/10.1007/s11253-014-0918-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-014-0918-7

Keywords

Navigation