Algebraic Numbers

• Autorzy: Yasushige Watase
• Języki publikacji: EN

Abstrakty

EN

This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well. As an application of an algebraic number, this article includes a formal proof of a ring extension of rational number field ℚ induced by substitution of an algebraic number to the polynomial ring of ℚ[x] turns to be a field.

Słowa kluczowe

EN

algebraic number; integral dependency

Kategorie tematyczne

• 03B35: Mechanization of proofs and logical operations
• 11R04: Algebraic numbers; rings of algebraic integers
• 13B21: Integral dependence; going up, going down

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2016
• Tom: 24
• Numer: 4
• Strony: 291-299

Daty

wydano

2016-12-01

otrzymano

2016-12-15

online

2017-02-23

Twórcy

autor

Yasushige Watase

• Suginami-ku Matsunoki 6, 3-21 Tokyo,

Identyfikatory

DOI

10.1515/forma-2016-0025