On Roots of Polynomials and Algebraically Closed Fields

Christoph Schwarzweller. "On Roots of Polynomials and Algebraically Closed Fields." Formalized Mathematics 25.3 (2017): 185-195. <http://eudml.org/doc/288477>.

@article{ChristophSchwarzweller2017,
abstract = {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].},
author = {Christoph Schwarzweller},
journal = {Formalized Mathematics},
keywords = {commutative algebra; polynomials; algebraic closed fields},
language = {eng},
number = {3},
pages = {185-195},
title = {On Roots of Polynomials and Algebraically Closed Fields},
url = {http://eudml.org/doc/288477},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Christoph Schwarzweller
TI - On Roots of Polynomials and Algebraically Closed Fields
JO - Formalized Mathematics
PY - 2017
VL - 25
IS - 3
SP - 185
EP - 195
AB - 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].
LA - eng
KW - commutative algebra; polynomials; algebraic closed fields
UR - http://eudml.org/doc/288477
ER -