The First Isomorphism Theorem and Other Properties of Rings

Pole DC	Wartość	Język
dc.contributor.author	Korniłowicz, Artur	-
dc.contributor.author	Schwarzweller, Christoph	-
dc.date.accessioned	2015-12-09T20:41:41Z	-
dc.date.available	2015-12-09T20:41:41Z	-
dc.date.issued	2014	-
dc.identifier.citation	Formalized Mathematics, Volume 22, Issue 4, 2014, Pages 291-301	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3725	-
dc.description.abstract	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 → S we have R/ker(f) ≅ 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.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	commutative algebra	-
dc.subject	ring theory	-
dc.subject	first isomorphism theorem	-
dc.title	The First Isomorphism Theorem and Other Properties of Rings	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2014-0029	-
dc.description.Affiliation	Korniłowicz Artur - Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland	-
dc.description.Affiliation	Schwarzweller Christoph - Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk Poland	-
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