Abstract Algebra : Splitting Fields

Study concepts, example questions & explanations for Abstract Algebra

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Example Questions

Example Question #1 : Splitting Fields

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:

Ideals Theorem

Principal Ideal Domain

Primitive Field Theorem

Gauss's Lemma

Eisenstein's Irreducibility Criterion

Correct answer:

Eisenstein's Irreducibility Criterion


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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