Category:Definitions/Field Extensions
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This category contains definitions related to Field Extensions.
Related results can be found in Category:Field Extensions.
Let $F$ be a field.
A field extension over $F$ is a field $E$ where $F \subseteq E$.
That is, such that $F$ is a subfield of $E$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
A
- Definitions/Adjoined Numbers (1 P)
G
Pages in category "Definitions/Field Extensions"
The following 66 pages are in this category, out of 66 total.
A
- Definition:Adjoined Number
- Definition:Algebraic Element of Field Extension
- Definition:Algebraic Element of Field Extension/Definition 1
- Definition:Algebraic Element of Field Extension/Definition 2
- Definition:Algebraic Field Extension
- Definition:Algebraic Number over Field/Degree
- Definition:Algebraic over Field
- Definition:Algebraically Closed Field
- Definition:Algebraically Closed Field/Definition 1
- Definition:Algebraically Closed Field/Definition 2
- Definition:Algebraically Closed Field/Definition 3
- Definition:Algebraically Independent
F
- Definition:Field Extension
- Definition:Field Extension/Also known as
- Definition:Field Extension/Complex
- Definition:Field Extension/Degree
- Definition:Field Extension/Degree/Finite
- Definition:Field Extension/Degree/Infinite
- Definition:Finite Field Extension
- Definition:Finitely Generated Field Extension
G
I
N
P
R
S
- Definition:Separable Closure
- Definition:Separable Degree
- Definition:Separable Element
- Definition:Separable Extension
- Definition:Separably Closed Field
- Definition:Simple Algebraic Field Extension
- Definition:Simple Field Extension
- Definition:Smallest Field containing Subfield and Complex Number
- Definition:Smallest Field containing Subfield and Complex Number/General Definition
T
- Definition:Tower of Fields
- Definition:Transcendence Degree
- Definition:Transcendental
- Definition:Transcendental (Abstract Algebra)
- Definition:Transcendental (Abstract Algebra)/Field Extension
- Definition:Transcendental (Abstract Algebra)/Field Extension/Element
- Definition:Transcendental Element of Field Extension
- Definition:Transcendental Field Extension
- Definition:Transcendental over Field