Conservation Rules of Direct Sum Decomposition of Groups

Kazuhisa Nakasho; Hiroshi Yamazaki; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2016)

  • Volume: 24, Issue: 1, page 81-94
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Kazuhisa Nakasho, et al. "Conservation Rules of Direct Sum Decomposition of Groups." Formalized Mathematics 24.1 (2016): 81-94. <http://eudml.org/doc/286760>.

@article{KazuhisaNakasho2016,
abstract = {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.},
author = {Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {group theory; direct sum decomposition},
language = {eng},
number = {1},
pages = {81-94},
title = {Conservation Rules of Direct Sum Decomposition of Groups},
url = {http://eudml.org/doc/286760},
volume = {24},
year = {2016},
}

TY - JOUR
AU - Kazuhisa Nakasho
AU - Hiroshi Yamazaki
AU - Hiroyuki Okazaki
AU - Yasunari Shidama
TI - Conservation Rules of Direct Sum Decomposition of Groups
JO - Formalized Mathematics
PY - 2016
VL - 24
IS - 1
SP - 81
EP - 94
AB - 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.
LA - eng
KW - group theory; direct sum decomposition
UR - http://eudml.org/doc/286760
ER -

References

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