The First Isomorphism Theorem and Other Properties of Rings

Artur Korniłowicz; Christoph Schwarzweller

doi:10.2478/forma-2014-0029

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The First Isomorphism Theorem and Other Properties of Rings

Formalized Mathematics

Volume 22 (2014): Issue 4 (December 2014)

By: Artur Korniłowicz and Christoph Schwarzweller

Open Access

|Dec 2014

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

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Articles in this issue

DOI: https://doi.org/10.2478/forma-2014-0029 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 291 - 301

Submitted on: Nov 29, 2014

Published on: Dec 31, 2014

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

commutative algebra,

ring theory,

first isomorphism theorem

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2014 Artur Korniłowicz, Christoph Schwarzweller, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Volume 22 (2014): Issue 4 (December 2014)