# On Roots of Polynomials and Algebraically Closed Fields

Formalized Mathematics (2017)

- Volume: 25, Issue: 3, page 185-195
- ISSN: 1426-2630

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topChristoph 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 -

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