{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T11:04:47Z","timestamp":1774868687225,"version":"3.50.1"},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9,1]]},"abstract":"Summary<\/jats:title>\n \n In this article we prove the well-known characterization of finite Galois extensions: a finite extension\n E<\/jats:italic>\n of\n F<\/jats:italic>\n is a Galois extension of\n F<\/jats:italic>\n i\n E<\/jats:italic>\n is both normal and separable i\n E<\/jats:italic>\n is the splitting field of a separable polynomial\n p<\/jats:italic>\n \u2208\n F<\/jats:italic>\n [\n X<\/jats:italic>\n ]. We also prove some applications of the characterization, so for example that\n F<\/jats:italic>\n (\n a<\/jats:italic>\n 1<\/jats:sub>\n , . . .,\n \n a\n n<\/jats:sub>\n <\/jats:italic>\n ) is a separable extension of\n F<\/jats:italic>\n if and only if all the\n a<\/jats:italic>\n i<\/jats:sub>\n are separable, or that every finite separable extension of\n F<\/jats:italic>\n is contained in a Galois extension of\n F<\/jats:italic>\n .\n <\/jats:p>","DOI":"10.2478\/forma-2025-0019","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T16:26:24Z","timestamp":1767975984000},"page":"237-244","source":"Crossref","is-referenced-by-count":0,"title":["Characterization of Finite Galois Extensions"],"prefix":"10.2478","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9587-8737","authenticated-orcid":false,"given":"Christoph","family":"Schwarzweller","sequence":"first","affiliation":[{"name":"Institute of Informatics University of Gda\u0144sk , Poland"}]}],"member":"374","published-online":{"date-parts":[[2025,12,31]]},"reference":[{"key":"2026033010152309669_j_forma-2025-0019_ref_001","unstructured":"David S. 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Springer-Verlag, second edition, 2009.","DOI":"10.1007\/978-0-387-87575-0"}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.sciendo.com\/pdf\/10.2478\/forma-2025-0019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T10:15:40Z","timestamp":1774865740000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.2478\/forma-2025-0019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,1]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12,31]]},"published-print":{"date-parts":[[2025,9,1]]}},"alternative-id":["10.2478\/forma-2025-0019"],"URL":"https:\/\/doi.org\/10.2478\/forma-2025-0019","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,1]]}}}