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Formalized Mathematics

(a computer assisted approach)

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Volume 24, Issue 1 (Mar 2016)


Conservation Rules of Direct Sum Decomposition of Groups

Kazuhisa Nakasho
  • Corresponding author
  • Shinshu University Nagano, Japan
/ Hiroshi Yamazaki
  • Shinshu University Nagano, Japan
/ Hiroyuki Okazaki
  • Shinshu University Nagano, Japan
/ Yasunari Shidama
  • Shinshu University Nagano, Japan
Published Online: 2016-08-31 | DOI: https://doi.org/10.1515/forma-2016-0007


In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization.

MSC: 20E34; 03B35

Keywords: group theory; direct sum decomposition

MML : identifier: GROUP 21; version: 8.1.04 5.36.1267


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About the article

Received: 2015-12-31

Published Online: 2016-08-31

Published in Print: 2016-03-01

Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2016-0007. Export Citation

© by Kazuhisa Nakasho. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

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