# Equivalent Expressions of Direct Sum Decomposition of Groups1

Kazuhisa Nakasho; Hiroyuki Okazaki; Hiroshi Yamazaki; Yasunari Shidama

Formalized Mathematics (2015)

- Volume: 23, Issue: 1, page 67-73
- ISSN: 1426-2630

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topKazuhisa Nakasho, et al. "Equivalent Expressions of Direct Sum Decomposition of Groups1." Formalized Mathematics 23.1 (2015): 67-73. <http://eudml.org/doc/270901>.

@article{KazuhisaNakasho2015,

abstract = {In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.},

author = {Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, Yasunari Shidama},

journal = {Formalized Mathematics},

keywords = {group theory; direct sum decomposition; direct sums of groups; direct sum decompositions},

language = {eng},

number = {1},

pages = {67-73},

title = {Equivalent Expressions of Direct Sum Decomposition of Groups1},

url = {http://eudml.org/doc/270901},

volume = {23},

year = {2015},

}

TY - JOUR

AU - Kazuhisa Nakasho

AU - Hiroyuki Okazaki

AU - Hiroshi Yamazaki

AU - Yasunari Shidama

TI - Equivalent Expressions of Direct Sum Decomposition of Groups1

JO - Formalized Mathematics

PY - 2015

VL - 23

IS - 1

SP - 67

EP - 73

AB - In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.

LA - eng

KW - group theory; direct sum decomposition; direct sums of groups; direct sum decompositions

UR - http://eudml.org/doc/270901

ER -

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