<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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]/&lt;p> is isomorphic to the field of polynomials with degree smaller than the one of p.</p></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.

Some Algebraic Properties of Polynomial Rings

Institute of Computer Science University of Gdansk,

Institute of Informatics University of Białystok,

Formalized Mathematics

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License

{"article-title":"Some Algebraic Properties of Polynomial Rings"}

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]/ is isomorphic to the field of polynomials with degree smaller than the one of p.

In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic...

Some Algebraic Properties of Polynomial Rings

Online veröffentlicht: 21. Feb. 2017

Seitenbereich: 227 - 237

Eingereicht: 30. Juni 2016

DOI: https://doi.org/10.1515/forma-2016-0019

Schlüsselwörter
polynomial, polynomial ring, polynomial GCD

© by Christoph Schwarzweller

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License

Some Algebraic Properties of Polynomial Rings

Online veröffentlicht: 21. Feb. 2017

Seitenbereich: 227 - 237

Eingereicht: 30. Juni 2016

DOI: https://doi.org/10.1515/forma-2016-0019

Schlüsselwörterpolynomial, polynomial ring, polynomial GCD

© by Christoph Schwarzweller

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License

Schlüsselwörter
polynomial, polynomial ring, polynomial GCD