Some Algebraic Properties of Polynomial Rings
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.
Language: English
Page range: 227 - 237
Submitted on: Jun 30, 2016
Published on: Feb 21, 2017
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
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© 2017 Christoph Schwarzweller, Artur Korniłowicz, Agnieszka Rowinska-Schwarzweller, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.