Definition and Properties of Direct Sum Decomposition of Groups1

• Autorzy: Kazuhisa Nakasho , Hiroshi Yamazaki , Hiroyuki Okazaki , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal direct sum is proved. We referred to [23], [22], [8] and [18] in the formalization.

Słowa kluczowe

EN

group theory; direct sum decomposition

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 20E34: General structure theorems

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 1
• Strony: 15-27

Daty

wydano

2015-03-01

otrzymano

2014-12-31

online

2015-03-31

Twórcy

autor

Kazuhisa Nakasho

• Shinshu University, Nagano, Japan

autor

Hiroshi Yamazaki

• Shinshu University, Nagano, Japan

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

Bibliografia

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Identyfikatory

DOI

10.2478/forma-2015-0002

bwmeta1.id-class.MML

GROUP_19