Eintrag weiter verarbeiten
Definition and Properties of Direct Sum Decomposition of Groups1
Gespeichert in:
| Zeitschriftentitel: | Formalized Mathematics |
|---|---|
| Personen und Körperschaften: | , , , |
| In: | Formalized Mathematics, 23, 2015, 1, S. 15-27 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Walter de Gruyter GmbH
|
| Schlagwörter: |
| author_facet |
Nakasho, Kazuhisa Yamazaki, Hiroshi Okazaki, Hiroyuki Shidama, Yasunari Nakasho, Kazuhisa Yamazaki, Hiroshi Okazaki, Hiroyuki Shidama, Yasunari |
|---|---|
| author |
Nakasho, Kazuhisa Yamazaki, Hiroshi Okazaki, Hiroyuki Shidama, Yasunari |
| spellingShingle |
Nakasho, Kazuhisa Yamazaki, Hiroshi Okazaki, Hiroyuki Shidama, Yasunari Formalized Mathematics Definition and Properties of Direct Sum Decomposition of Groups1 Applied Mathematics Computational Mathematics |
| author_sort |
nakasho, kazuhisa |
| spelling |
Nakasho, Kazuhisa Yamazaki, Hiroshi Okazaki, Hiroyuki Shidama, Yasunari 1898-9934 Walter de Gruyter GmbH Applied Mathematics Computational Mathematics http://dx.doi.org/10.2478/forma-2015-0002 <jats:title>Summary</jats:title> <jats:p>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.</jats:p> Definition and Properties of Direct Sum Decomposition of Groups<sup>1</sup> Formalized Mathematics |
| doi_str_mv |
10.2478/forma-2015-0002 |
| facet_avail |
Online Free |
| finc_class_facet |
Mathematik |
| format |
ElectronicArticle |
| fullrecord |
blob:ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMjQ3OC9mb3JtYS0yMDE1LTAwMDI |
| id |
ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMjQ3OC9mb3JtYS0yMDE1LTAwMDI |
| institution |
DE-Gla1 DE-Zi4 DE-15 DE-Pl11 DE-Rs1 DE-105 DE-14 DE-Ch1 DE-L229 DE-D275 DE-Bn3 DE-Brt1 DE-Zwi2 DE-D161 |
| imprint |
Walter de Gruyter GmbH, 2015 |
| imprint_str_mv |
Walter de Gruyter GmbH, 2015 |
| issn |
1898-9934 |
| issn_str_mv |
1898-9934 |
| language |
English |
| mega_collection |
Walter de Gruyter GmbH (CrossRef) |
| match_str |
nakasho2015definitionandpropertiesofdirectsumdecompositionofgroups1 |
| publishDateSort |
2015 |
| publisher |
Walter de Gruyter GmbH |
| recordtype |
ai |
| record_format |
ai |
| series |
Formalized Mathematics |
| source_id |
49 |
| title |
Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_unstemmed |
Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_full |
Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_fullStr |
Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_full_unstemmed |
Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_short |
Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_sort |
definition and properties of direct sum decomposition of groups<sup>1</sup> |
| topic |
Applied Mathematics Computational Mathematics |
| url |
http://dx.doi.org/10.2478/forma-2015-0002 |
| publishDate |
2015 |
| physical |
15-27 |
| description |
<jats:title>Summary</jats:title>
<jats:p>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.</jats:p> |
| container_issue |
1 |
| container_start_page |
15 |
| container_title |
Formalized Mathematics |
| container_volume |
23 |
| format_de105 |
Article, E-Article |
| format_de14 |
Article, E-Article |
| format_de15 |
Article, E-Article |
| format_de520 |
Article, E-Article |
| format_de540 |
Article, E-Article |
| format_dech1 |
Article, E-Article |
| format_ded117 |
Article, E-Article |
| format_degla1 |
E-Article |
| format_del152 |
Buch |
| format_del189 |
Article, E-Article |
| format_dezi4 |
Article |
| format_dezwi2 |
Article, E-Article |
| format_finc |
Article, E-Article |
| format_nrw |
Article, E-Article |
| _version_ |
1792343921409392642 |
| geogr_code |
not assigned |
| last_indexed |
2024-03-01T16:59:23.329Z |
| geogr_code_person |
not assigned |
| openURL |
url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fvufind.svn.sourceforge.net%3Agenerator&rft.title=Definition+and+Properties+of+Direct+Sum+Decomposition+of+Groups1&rft.date=2015-03-01&genre=article&issn=1898-9934&volume=23&issue=1&spage=15&epage=27&pages=15-27&jtitle=Formalized+Mathematics&atitle=Definition+and+Properties+of+Direct+Sum+Decomposition+of+Groups%3Csup%3E1%3C%2Fsup%3E&aulast=Shidama&aufirst=Yasunari&rft_id=info%3Adoi%2F10.2478%2Fforma-2015-0002&rft.language%5B0%5D=eng |
| SOLR | |
| _version_ | 1792343921409392642 |
| author | Nakasho, Kazuhisa, Yamazaki, Hiroshi, Okazaki, Hiroyuki, Shidama, Yasunari |
| author_facet | Nakasho, Kazuhisa, Yamazaki, Hiroshi, Okazaki, Hiroyuki, Shidama, Yasunari, Nakasho, Kazuhisa, Yamazaki, Hiroshi, Okazaki, Hiroyuki, Shidama, Yasunari |
| author_sort | nakasho, kazuhisa |
| container_issue | 1 |
| container_start_page | 15 |
| container_title | Formalized Mathematics |
| container_volume | 23 |
| description | <jats:title>Summary</jats:title> <jats:p>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.</jats:p> |
| doi_str_mv | 10.2478/forma-2015-0002 |
| facet_avail | Online, Free |
| finc_class_facet | Mathematik |
| format | ElectronicArticle |
| format_de105 | Article, E-Article |
| format_de14 | Article, E-Article |
| format_de15 | Article, E-Article |
| format_de520 | Article, E-Article |
| format_de540 | Article, E-Article |
| format_dech1 | Article, E-Article |
| format_ded117 | Article, E-Article |
| format_degla1 | E-Article |
| format_del152 | Buch |
| format_del189 | Article, E-Article |
| format_dezi4 | Article |
| format_dezwi2 | Article, E-Article |
| format_finc | Article, E-Article |
| format_nrw | Article, E-Article |
| geogr_code | not assigned |
| geogr_code_person | not assigned |
| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMjQ3OC9mb3JtYS0yMDE1LTAwMDI |
| imprint | Walter de Gruyter GmbH, 2015 |
| imprint_str_mv | Walter de Gruyter GmbH, 2015 |
| institution | DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161 |
| issn | 1898-9934 |
| issn_str_mv | 1898-9934 |
| language | English |
| last_indexed | 2024-03-01T16:59:23.329Z |
| match_str | nakasho2015definitionandpropertiesofdirectsumdecompositionofgroups1 |
| mega_collection | Walter de Gruyter GmbH (CrossRef) |
| physical | 15-27 |
| publishDate | 2015 |
| publishDateSort | 2015 |
| publisher | Walter de Gruyter GmbH |
| record_format | ai |
| recordtype | ai |
| series | Formalized Mathematics |
| source_id | 49 |
| spelling | Nakasho, Kazuhisa Yamazaki, Hiroshi Okazaki, Hiroyuki Shidama, Yasunari 1898-9934 Walter de Gruyter GmbH Applied Mathematics Computational Mathematics http://dx.doi.org/10.2478/forma-2015-0002 <jats:title>Summary</jats:title> <jats:p>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.</jats:p> Definition and Properties of Direct Sum Decomposition of Groups<sup>1</sup> Formalized Mathematics |
| spellingShingle | Nakasho, Kazuhisa, Yamazaki, Hiroshi, Okazaki, Hiroyuki, Shidama, Yasunari, Formalized Mathematics, Definition and Properties of Direct Sum Decomposition of Groups1, Applied Mathematics, Computational Mathematics |
| title | Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_full | Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_fullStr | Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_full_unstemmed | Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_short | Definition and Properties of Direct Sum Decomposition of Groups1 |
| title_sort | definition and properties of direct sum decomposition of groups<sup>1</sup> |
| title_unstemmed | Definition and Properties of Direct Sum Decomposition of Groups1 |
| topic | Applied Mathematics, Computational Mathematics |
| url | http://dx.doi.org/10.2478/forma-2015-0002 |