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Example Questions
Example Question #2 : Abstract Algebra
What definition does the following correlate to?
If is a prime, then the following polynomial is irreducible over the field of rational numbers.
Possible Answers:
Eisenstein's Irreducibility Criterion
Ideals Theorem
Principal Ideal Domain
Primitive Field Theorem
Gauss's Lemma
Correct answer:
Eisenstein's Irreducibility Criterion
Explanation:
The Eisenstein's Irreducibility Criterion is the theorem for which the given statement is a corollary to.
The Eisenstein's Irreducibility Criterion is as follows.
is a polynomial with coefficients that are integers. If there is a prime number that satisfy the following,
Then over the field of rational numbers is said to be irreducible.
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