{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T20:49:35Z","timestamp":1648759775947},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2015,6,1]],"date-time":"2015-06-01T00:00:00Z","timestamp":1433116800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We 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 Korni\u0142owicz [25]. <\/jats:p>\n               <jats:p>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\u2019s theorem and some other theorems concerning these notions [9, 24, 22] are presented. <\/jats:p>\n               <jats:p>Note that \u201cThe term \u2124-module is simply another name for an additive abelian group\u201d [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 Korni\u0142owicz [25]. Indeed, H\u00f6lzl et al. showed that it was possible to build \u201ca generic theory of limits based on filters\u201d 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.<\/jats:p>","DOI":"10.1515\/forma-2015-0013","type":"journal-article","created":{"date-parts":[[2015,8,14]],"date-time":"2015-08-14T20:14:57Z","timestamp":1439583297000},"page":"127-160","source":"Crossref","is-referenced-by-count":1,"title":["Groups \u2013 Additive Notation"],"prefix":"10.1515","volume":"23","author":[{"given":"Roland","family":"Coghetto","sequence":"first","affiliation":[{"name":"Rue de la Brasserie 5 7100 La Louvi\u00e8re, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2015,8,13]]},"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/23\/2\/article-p127.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2015-0013","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T03:21:59Z","timestamp":1617938519000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2015-0013"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,8,13]]},"published-print":{"date-parts":[[2015,6,1]]}},"alternative-id":["10.1515\/forma-2015-0013"],"URL":"https:\/\/doi.org\/10.1515\/forma-2015-0013","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,1]]}}}