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  3. Formalized Mathematics
  4. Formalized Mathematics, 2012, Volume 20, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3658
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    Pole DCWartośćJęzyk
    dc.contributor.authorArai, Kenichi-
    dc.contributor.authorOkazaki, Hiroyuki-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2015-12-06T19:06:10Z-
    dc.date.available2015-12-06T19:06:10Z-
    dc.date.issued2012-
    dc.identifier.citationFormalized Mathematics, Volume 20, Issue 4, 2012, Pages 343-347-
    dc.identifier.issn1426-2630-
    dc.identifier.issn1898-9934-
    dc.identifier.urihttp://hdl.handle.net/11320/3658-
    dc.description.abstractIn this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.-
    dc.language.isoen-
    dc.publisherDe Gruyter Open-
    dc.titleIsomorphisms of Direct Products of Finite Cyclic Groups-
    dc.typeArticle-
    dc.identifier.doi10.2478/v10037-012-0038-5-
    dc.description.AffiliationArai Kenichi - Tokyo University of Science, Chiba, Japan-
    dc.description.AffiliationOkazaki Hiroyuki - Shinshu University, Nagano, Japan-
    dc.description.AffiliationShidama Yasunari - Shinshu University, Nagano, Japan-
    dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.-
    dc.description.referencesGrzegorz Bancerek. K¨onig’s theorem. Formalized Mathematics, 1(3):589-593, 1990.-
    dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
    dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.-
    dc.description.referencesCzesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.-
    dc.description.referencesCzesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.-
    dc.description.referencesCzesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.-
    dc.description.referencesCzesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.-
    dc.description.referencesCzesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.-
    dc.description.referencesCzesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.-
    dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.-
    dc.description.referencesAndrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.-
    dc.description.referencesArtur Korniłowicz. On the real valued functions. Formalized Mathematics, 13(1):181-187, 2005.-
    dc.description.referencesEugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.-
    dc.description.referencesAnna Lango and Grzegorz Bancerek. Product of families of groups and vector spaces. Formalized Mathematics, 3(2):235-240, 1992.-
    dc.description.referencesHiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics, 19(1):51-59, 2011, doi: 10.2478/v10037-011-0009-2.-
    dc.description.referencesChristoph Schwarzweller. The ring of integers, Euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.-
    dc.description.referencesChristoph Schwarzweller. Modular integer arithmetic. Formalized Mathematics, 16(3):247-252, 2008, doi:10.2478/v10037-008-0029-8.-
    dc.description.referencesAndrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.-
    dc.description.referencesMichał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.-
    dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.-
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.-
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.-
    Występuje w kolekcji(ach):Formalized Mathematics, 2012, Volume 20, Issue 4

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