Algebraic Numbers

Yasushige Watase. "Algebraic Numbers." Formalized Mathematics 24.4 (2016): 291-299. <http://eudml.org/doc/288072>.

@article{YasushigeWatase2016,
abstract = {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.},
author = {Yasushige Watase},
journal = {Formalized Mathematics},
keywords = {algebraic number; integral dependency},
language = {eng},
number = {4},
pages = {291-299},
title = {Algebraic Numbers},
url = {http://eudml.org/doc/288072},
volume = {24},
year = {2016},
}

TY - JOUR
AU - Yasushige Watase
TI - Algebraic Numbers
JO - Formalized Mathematics
PY - 2016
VL - 24
IS - 4
SP - 291
EP - 299
AB - 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.
LA - eng
KW - algebraic number; integral dependency
UR - http://eudml.org/doc/288072
ER -