{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T01:06:01Z","timestamp":1777424761892,"version":"3.51.4"},"reference-count":3,"publisher":"Walter de Gruyter GmbH","issue":"3","license":[{"start":{"date-parts":[[2016,9,1]],"date-time":"2016-09-01T00:00:00Z","timestamp":1472688000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0\/legalcode"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p> In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]\/&lt;p&gt; is isomorphic to the field of polynomials with degree smaller than the one of p.<\/jats:p>","DOI":"10.1515\/forma-2016-0019","type":"journal-article","created":{"date-parts":[[2017,2,14]],"date-time":"2017-02-14T10:02:03Z","timestamp":1487066523000},"page":"227-237","source":"Crossref","is-referenced-by-count":4,"title":["Some Algebraic Properties of Polynomial Rings"],"prefix":"10.1515","volume":"24","author":[{"given":"Christoph","family":"Schwarzweller","sequence":"first","affiliation":[{"name":"Institute of Computer Science University of Gdansk, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Artur","family":"Korni\u0142owicz","sequence":"additional","affiliation":[{"name":"Institute of Informatics University of Bia\u0142ystok, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Agnieszka","family":"Rowinska-Schwarzweller","sequence":"additional","affiliation":[{"name":"Sopot Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,2,21]]},"reference":[{"key":"2021040807371567274_j_forma-2016-0019_ref_1_w2aab2b8b2b1b7b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] Grzegorz Bancerek, Czes\u0142aw Bylinski, Adam Grabowski, Artur Korni\u0142owicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007\/978-3-319-20615-8_17.","DOI":"10.1007\/978-3-319-20615-8_17"},{"key":"2021040807371567274_j_forma-2016-0019_ref_2_w2aab2b8b2b1b7b1ab1ab2Aa","doi-asserted-by":"crossref","unstructured":"[2] H. Heuser. Lehrbuch der Analysis. B.G. Teubner Stuttgart, 1990.","DOI":"10.1007\/978-3-663-12214-2"},{"key":"2021040807371567274_j_forma-2016-0019_ref_3_w2aab2b8b2b1b7b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"[3] Steven H. Weintraub. Galois Theory. Springer Verlag, 2 edition, 2009.","DOI":"10.1007\/978-0-387-87575-0"}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/24\/3\/article-p227.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2016-0019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T02:04:30Z","timestamp":1617933870000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2016-0019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,1]]},"references-count":3,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,2,21]]},"published-print":{"date-parts":[[2016,9,1]]}},"alternative-id":["10.1515\/forma-2016-0019"],"URL":"https:\/\/doi.org\/10.1515\/forma-2016-0019","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,1]]}}}