Inner Products, Group, Ring of Quaternion Numbers

Fuguo Ge

Formalized Mathematics (2008)

  • Volume: 16, Issue: 2, page 135-139
  • ISSN: 1426-2630

Abstract

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In this article, we define the division of the quaternion numbers, we also give the definition of inner products, group, ring of the quaternion numbers, and we prove some of their properties.MML identifier: QUATERN2, version: 7.8.10 4.100.1011

How to cite

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Fuguo Ge. "Inner Products, Group, Ring of Quaternion Numbers." Formalized Mathematics 16.2 (2008): 135-139. <http://eudml.org/doc/267236>.

@article{FuguoGe2008,
abstract = {In this article, we define the division of the quaternion numbers, we also give the definition of inner products, group, ring of the quaternion numbers, and we prove some of their properties.MML identifier: QUATERN2, version: 7.8.10 4.100.1011},
author = {Fuguo Ge},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {135-139},
title = {Inner Products, Group, Ring of Quaternion Numbers},
url = {http://eudml.org/doc/267236},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Fuguo Ge
TI - Inner Products, Group, Ring of Quaternion Numbers
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 2
SP - 135
EP - 139
AB - In this article, we define the division of the quaternion numbers, we also give the definition of inner products, group, ring of the quaternion numbers, and we prove some of their properties.MML identifier: QUATERN2, version: 7.8.10 4.100.1011
LA - eng
UR - http://eudml.org/doc/267236
ER -

References

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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  3. [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  4. [4] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  5. [5] Xiquan Liang and Fuguo Ge. The quaternion numbers. Formalized Mathematics, 14(4):161-169, 2006. 
  6. [6] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990. 
  7. [7] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  8. [8] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  9. [9] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 

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