
Extension Fields and Transcendental Numbers
Authored by DEEPA BALAN
Mathematics
University
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25 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is an extension field?
A field containing a subfield
A set of numbers closed under addition and multiplication
A field that is a subset of another field
A field with more elements than its subfield
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If F⊆E , what is the degree of the extension [E:F][E : F]?
The number of elements in E
The number of elements in F
The dimension of E as a vector space over F
The degree of the minimal polynomial of E
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is true for a simple extension field?
It is generated by a single element
It contains infinitely many elements
It is always finite
It is always algebraic
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If E is a finite extension of F, then E is:
Algebraic over FF
Transcendental over FF
Both algebraic and transcendental
Neither algebraic nor transcendental
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is a property of a Galois extension?
It is always finite
It is always algebraic
It is always normal and separable
It is always transcendental
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is true for a finite extension field?
It is always algebraic
It is always transcendental
It is both algebraic and transcendental
It is neither algebraic nor transcendental
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If E is a finite extension of F, then E is:
Algebraic over F
Transcendental over F
Both algebraic and transcendental
Neither algebraic nor transcendental
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