algebraic element (C1)
noun phrase
Pronunciation: /ˌældʒɪˈbrɛɪɪk ˈɛlɪmənt/
Definition
A mathematical object that can be expressed as a root of a polynomial equation with rational coefficients, and is used to extend the field of rational numbers to include roots of polynomials.
Examples
The algebraic elements of a field extension are precisely the roots of non-constant polynomials with coefficients in the base field.
In algebraic geometry, algebraic elements are used to study the properties of curves and surfaces.
The set of algebraic elements of a field is a subfield, known as the algebraic closure of the field.
How to Use algebraic element
- algebraic element of a field (noun phrase)
- a root of a polynomial equation with rational coefficients — "The algebraic elements of a field extension are precisely the roots of non-constant polynomials with coefficients in the base field."
- algebraic element of a curve (noun phrase)
- a point on a curve defined by polynomial equations — "The algebraic elements of a curve are the points where the curve intersects itself or other curves."
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