The First Isomorphism Theorem and Other Properties of Rings
Artur Korniłowicz ; Christoph Schwarzweller
Formalized Mathematics, Tome 22 (2014), p. 291-301 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:270996
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     author = {Artur Korni\l owicz and Christoph Schwarzweller},
     title = {The First Isomorphism Theorem and Other Properties of Rings},
     journal = {Formalized Mathematics},
     volume = {22},
     year = {2014},
     pages = {291-301},
     zbl = {1316.13003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0029}
}
Artur Korniłowicz; Christoph Schwarzweller. The First Isomorphism Theorem and Other Properties of Rings. Formalized Mathematics, Tome 22 (2014) pp. 291-301. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2014-0029/

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