The First Isomorphism Theorem and Other Properties of Rings

Artur Korniłowicz 1  and Christoph Schwarzweller 2
  • 1 Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland
  • 2 Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk Poland

Summary

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

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