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Some Algebraic Properties of Polynomial Rings

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Schwarzweller C., Korniłowicz A.

Formalized Mathematics

2016

tom 24

nr 3

227-237

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.

Ograniczanie wyników

1 Formalized Mathematics

1 Korniłowicz A.

1 Schwarzweller C.

1 2016

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Some Algebraic Properties of Polynomial Rings