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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
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Volume 21, Issue 2 (Jun 2013)

Issues

Gaussian Integers

*

Yuichi Futa / Hiroyuki Okazaki / Daichi Mizushima
  • Shinshu University Nagano, Japan
  • This research was presented during the 2012 International Symposium on Information Theory and its Applications (ISITA2012) in Honolulu, USA.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Yasunari Shidama

Summary

Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational number field and a quotient field of the Gaussian integer ring are isomorphic.

Keywords: formalization of Gaussian integers; algebraic integers

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About the article

Published in Print: 2013-06-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/forma-2013-0013.

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