{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T06:02:13Z","timestamp":1779775333082,"version":"3.53.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2014,12,1]],"date-time":"2014-12-01T00:00:00Z","timestamp":1417392000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Different properties of rings and fields are discussed [12], [41] and [17]. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R \u2192 S we have R\/ker(f) \u2245 Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and hence also factorial<\/jats:p>","DOI":"10.2478\/forma-2014-0029","type":"journal-article","created":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T13:39:57Z","timestamp":1434461997000},"page":"291-301","source":"Crossref","is-referenced-by-count":13,"title":["The First Isomorphism Theorem and Other Properties of Rings"],"prefix":"10.2478","volume":"22","author":[{"given":"Artur","family":"Korni\u0142owicz","sequence":"first","affiliation":[{"name":"Institute of Informatics University of Bia\u0142ystok Sosnowa 64, 15-887 Bia\u0142ystok Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christoph","family":"Schwarzweller","sequence":"additional","affiliation":[{"name":"Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2014,12,31]]},"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/22\/4\/article-p291.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/reference-global.com\/pdf\/10.2478\/forma-2014-0029","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T05:02:29Z","timestamp":1779771749000},"score":1,"resource":{"primary":{"URL":"https:\/\/reference-global.com\/article\/10.2478\/forma-2014-0029"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,1]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,12,31]]},"published-print":{"date-parts":[[2014,12,1]]}},"alternative-id":["10.2478\/forma-2014-0029"],"URL":"https:\/\/doi.org\/10.2478\/forma-2014-0029","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,1]]}}}