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http://hdl.handle.net/11320/4877
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Pole DC | Wartość | Język |
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dc.contributor.author | Coghetto, Roland | pl |
dc.date.accessioned | 2016-12-15T13:01:51Z | - |
dc.date.available | 2016-12-15T13:01:51Z | - |
dc.date.issued | 2015 | pl |
dc.identifier.citation | Formalized Mathematics, Volume 23, Issue 2, 127–160 | pl |
dc.identifier.issn | 1426-2630 | pl |
dc.identifier.issn | 1898-9934 | pl |
dc.identifier.uri | http://hdl.handle.net/11320/4877 | - |
dc.description.abstract | AbstractWe translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. In particular, these authors have defined the notions of group, abelian group, power of an element of a group, order of a group and order of an element, subgroup, coset of a subgroup, index of a subgroup, conjugation, normal subgroup, topological group, dense subset and basis of a topological group. Lagrange’s theorem and some other theorems concerning these notions [9, 24, 22] are presented. Note that “The term ℤ-module is simply another name for an additive abelian group” [27]. We take an approach different than that used by Futa et al. [21] to use in a future article the results obtained by Artur Korniłowicz [25]. Indeed, Hölzl et al. showed that it was possible to build “a generic theory of limits based on filters” in Isabelle/HOL [23, 10]. Our goal is to define the convergence of a sequence and the convergence of a series in an abelian topological group [11] using the notion of filters. | pl |
dc.language.iso | en | pl |
dc.publisher | De Gruyter Open | pl |
dc.subject | additive group; | pl |
dc.subject | subgroup; | pl |
dc.subject | Lagrange theorem; | pl |
dc.subject | conjugation; | pl |
dc.subject | normal subgroup; | pl |
dc.subject | index; | pl |
dc.subject | additive topological group; | pl |
dc.subject | basis; | pl |
dc.subject | neighborhood; | pl |
dc.subject | additive abelian group; | pl |
dc.subject | Z-module | pl |
dc.title | Groups – Additive Notation | pl |
dc.type | Article | pl |
dc.identifier.doi | 10.1515/forma-2015-0013 | pl |
dc.description.Affiliation | Rue de la Brasserie 5 7100 La Louvière, Belgium | pl |
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