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• # Artykuł - szczegóły

## Formalized Mathematics

2014 | 22 | 4 | 291-301

## The First Isomorphism Theorem and Other Properties of Rings

EN

### Abstrakty

EN
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

EN

291-301

wydano
2014-12-01
otrzymano
2014-11-29
online
2014-12-31

### Twórcy

autor
• Institute of Informatics University of Białystok Sosnowa 64, 15-887 Białystok Poland
• Institute of Computer Science University of Gdansk Wita Stwosza 57, 80-952 Gdansk Poland

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