On Roots of Polynomials and Algebraically Closed Fields

• Autorzy: Christoph Schwarzweller
• Języki publikacji: EN

Abstrakty

EN

In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].

Słowa kluczowe

EN

commutative algebra; polynomials; algebraic closed fields

Kategorie tematyczne

• 13B25: Polynomials over commutative rings
• 03B35: Mechanization of proofs and logical operations
• 13A05: Divisibility; factorizations

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2017
• Tom: 25
• Numer: 3
• Strony: 185-195

Daty

wydano

2017-10-01

otrzymano

2017-08-30

online

2017-12-19

Twórcy

autor

Christoph Schwarzweller

• , ,

Identyfikatory

DOI

10.1515/forma-2017-0018