Examples of 'algebraically closed' in a sentence
Meaning of "algebraically closed"
This phrase refers to a mathematical concept in algebra that describes a field in which all polynomial equations have solutions. It denotes a mathematical structure that satisfies certain closure properties, allowing for the complete algebraic manipulation of equations and expressions. The phrase is used in mathematical discussions, particularly within the field of abstract algebra and algebraic geometry
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- Which contains as an element every root of every nonconstant univariate polynomial definable over it (i.e., over said field).
How to use "algebraically closed" in a sentence
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algebraically closed
Any extension of an algebraically closed field is regular.
Prove that no finite field is algebraically closed.
No algebraically closed group is finitely generated.
It is a complete and algebraically closed field.
An infinite field is totally transcendental if and only if it is algebraically closed.
Let k be an algebraically closed field.
It is not necessary for the field to be algebraically closed.
Quasi algebraically closed field.
Now consider the class of algebraically closed fields.
Algebraically closed extension.
This is due to the fact that is algebraically closed.
It is algebraically closed.
A field with no nontrivial algebraic extensions is called algebraically closed.
Is an algebraically closed.
It relates algebraic sets to ideals in polynomial rings over algebraically closed fields.
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The theory of algebraically closed fields is the model completion of the theory of fields.
Ground field k is algebraically closed.
This can be rephrased by saying that the field of algebraic numbers is algebraically closed.
Algebraically closed fields are of Tsen rank zero.
The fact that the complex numbers are algebraically closed is required here.
Pseudo algebraically closed field A field in which every variety has a rational point.
The field of constructible numbers is quadratically closed but not algebraically closed.
The absolute Galois group of an algebraically closed field is trivial.
Any algebraically closed field of characteristic 0.
The full theorem generalizes to any algebraic variety over an algebraically closed field.
Weak form, algebraically closed field of coefficients.
There is some ambiguity here if K is not algebraically closed.
A pseudo algebraically closed field of characteristic zero is quasi-algebraically closed.
A finite field F is not algebraically closed.
In general, algebraically closed fields are easier to handle than non-algebraically closed ones.
For simplicity, assume k is algebraically closed.
Let k be an algebraically closed field and let Pn be the projective n-space over k.
Otherwise, it is not algebraically closed.
Any algebraically closed field such as the complex numbers has Rolle 's property.
Here an end is reached, as Cp is algebraically closed.
Algebraically closed fields with a ( Krull ) valuation are perhaps the most important example.
Because of this fact, C is called an algebraically closed field.
For groups realized over algebraically closed fields, there is a single conjugacy class of Borel subgroups.
Framework, where K need not be algebraically closed.
Assume k is algebraically closed of characteristic p = 0.
Equivalently ( by definition ), the theorem states that the field of complex numbers is algebraically closed.
More generally, let C be an algebraically closed field and x a variable.
The answer turns out to be " yes ", and we call such groups algebraically closed groups.
Example, Let k be an algebraically closed field of characteristic p > 0.
This construction works if C is replaced by any algebraically closed field C of characteristic zero . [ 4 ].
The first-order theory of algebraically closed fields of a given characteristic, established by Tarski in 1949.
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Examples of using Algebraically
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And we figured it out algebraically using substitution
But we could just figure it out algebraically
Any extension of an algebraically closed field is regular
Examples of using Closed
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The fairy has closed the path
They closed the school for good
Oven door must be closed while broiling
