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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 24, Issue 1 (Mar 2016)

Issues

Conservation Rules of Direct Sum Decomposition of Groups

Kazuhisa Nakasho / Hiroshi Yamazaki / Hiroyuki Okazaki / Yasunari Shidama
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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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.

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

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