Gaussian Integers

Yuichi Futa; Hiroyuki Okazaki; Daichi Mizushima; Yasunari Shidama

Formalized Mathematics (2013)

  • Volume: 21, Issue: 2, page 115-125
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Yuichi Futa, et al. "Gaussian Integers." Formalized Mathematics 21.2 (2013): 115-125. <http://eudml.org/doc/266545>.

@article{YuichiFuta2013,
abstract = {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.},
author = {Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {formalization of Gaussian integers; algebraic integers},
language = {eng},
number = {2},
pages = {115-125},
title = {Gaussian Integers},
url = {http://eudml.org/doc/266545},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Yuichi Futa
AU - Hiroyuki Okazaki
AU - Daichi Mizushima
AU - Yasunari Shidama
TI - Gaussian Integers
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 2
SP - 115
EP - 125
AB - 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.
LA - eng
KW - formalization of Gaussian integers; algebraic integers
UR - http://eudml.org/doc/266545
ER -

References

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