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.
@article{bwmeta1.element.doi-10_1515_forma-2016-0007,
author = {Kazuhisa Nakasho and Hiroshi Yamazaki and Hiroyuki Okazaki and Yasunari Shidama},
title = {Conservation Rules of Direct Sum Decomposition of Groups},
journal = {Formalized Mathematics},
volume = {24},
year = {2016},
pages = {81-94},
zbl = {1343.20033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0007}
}
Kazuhisa Nakasho; Hiroshi Yamazaki; Hiroyuki Okazaki; Yasunari Shidama. Conservation Rules of Direct Sum Decomposition of Groups. Formalized Mathematics, Tome 24 (2016) pp. 81-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_forma-2016-0007/
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