Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
See all formats and pricing
More options …
Volume 24, Issue 3

Issues

Some Algebraic Properties of Polynomial Rings

Christoph Schwarzweller / Artur Korniłowicz / Agnieszka Rowinska-Schwarzweller
Published Online: 2017-02-21 | DOI: https://doi.org/10.1515/forma-2016-0019

Abstract

In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/<p> is isomorphic to the field of polynomials with degree smaller than the one of p.

MSC: 12E05; 11T55; 03B35

Keywords: polynomial; polynomial ring; polynomial GCD

MML: identifier: RING_4; version: 8.1.05 5.37.1275

References

  • [1] Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: CrossrefGoogle Scholar

  • [2] H. Heuser. Lehrbuch der Analysis. B.G. Teubner Stuttgart, 1990.Google Scholar

  • [3] Steven H. Weintraub. Galois Theory. Springer Verlag, 2 edition, 2009.Google Scholar

About the article

Received: 2016-06-30

Published Online: 2017-02-21

Published in Print: 2016-09-01


Citation Information: Formalized Mathematics, Volume 24, Issue 3, Pages 227–237, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2016-0019.

Export Citation

© by Christoph Schwarzweller. This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License BY-SA 3.0 LEGALCODE

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Christoph Schwarzweller
Formalized Mathematics, 2017, Volume 25, Number 3

Comments (0)

Please log in or register to comment.
Log in