Examples of 'finite extension' in a sentence
Meaning of "finite extension"
finite extension: In mathematics, this phrase refers to a field extension in which the degree of the extension (i.e., the dimension of the extension as a vector space) is finite. It implies that the extension is limited in size or scope. The concept of finite extensions is significant in algebraic field theory and has applications in various branches of mathematics
How to use "finite extension" in a sentence
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finite extension
The field has no proper finite extension.
Every finite extension of a finite field is a cyclic extension.
So now let me take an arbitrary finite extension.
A finite extension is an extension that has a finite degree.
A field is called perfect if all finite extension fields are separable.
A finite extension of fields is an algebraic extension.
If a field is Ci then so is a finite extension.
Any finite extension of a finite field is a cyclic extension.
Perfect field A field such that every finite extension is separable.
Finite extension of the ground field.
Restriction of scalars over a finite extension of fields takes group schemes to group schemes.
Finite extension A finite extension is a field extension whose degree is finite.
In particular, every finite extension is algebraic.
For finite extension fields, it means the polynomial basis.
In particular, an algebraic integer is an integral element of a finite extension K / ℚ.
See also
Every finite extension of k is separable.
FF is not algebraically closed, but some finite extension is.
Let I be a finite extension of k of degree s.
Properties of the norm = = Several properties of the norm function hold for any finite extension.
E is a finite extension of F.
In particular, an algebraic integer is an integral element of a finite extension formula_18.
The Brauer group of a finite extension of a quasi-algebraically closed field is trivial.
Now, similarly, F generates the Galois group of any finite extension of.
Let K be a finite extension of the p-adic numbers Qp.
Each waypoint is an área with a finite extension ( circle or rectangle ).
Then Q ( √ d ) is a finite extension of Q of degree 2, called a quadratic extension.
So, K is a finite extension.
If " L " is a finite extension of " K ", then its normal closure is also a finite extension.
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Examples of using Finite
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The fixed and finite nature of land
All finite fields of a given order are isomorphic
A set that is not finite is called infinite
Examples of using Extension
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This second extension must be authorized by a judge
The applicant shall be informed of any extension
Do not use extension cords or multiple sockets
