Some Algebraic Properties of Polynomial Rings

• Autorzy: Christoph Schwarzweller , Artur Korniłowicz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

polynomial; polynomial ring; polynomial GCD

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2016
• Tom: 24
• Numer: 3
• Strony: 227-237

Daty

wydano

2016-09-01

otrzymano

2016-06-30

online

2017-02-08

Twórcy

autor

Christoph Schwarzweller

• Institute of Computer Science University of Gdansk,

autor

Artur Korniłowicz

• Institute of Informatics University of Białystok,

Identyfikatory

DOI

10.1515/forma-2016-0019