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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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In This Section
Volume 24, Issue 1 (Mar 2016)

Issues

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

Summary

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

References

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  • [5] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17. [Crossref]

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  • [12] Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, and Yasunari Shidama. Definition and properties of direct sum decomposition of groups. Formalized Mathematics, 23 (1):15-27, 2015. doi:10.2478/forma-2015-0002. [Crossref]

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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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