The First Isomorphism Theorem and Other Properties of Rings
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 th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2014-12-01
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| Series: | Formalized Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/forma-2014-0029 |
| 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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| ISSN: | 1898-9934 |