Lecture

Irreducible Polynomials and Finite Fields

In course

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Description

This lecture covers irreducible polynomials with coefficients in a field, the Eisenstein criterion, quotients of polynomial rings, the order of the quotient field, properties of finite fields, the splitting field of a polynomial, and the cyclic group of units of a finite field. It also explains how to construct a unique finite field of p^n elements as a quotient of F_p[x] over the ideal generated by an irreducible polynomial of degree n.

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_d0qmuenv

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Ontological neighbourhood

Mathematics

Algebra: Abstract algebra, Polynomials, Representation theory

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