Abstract Algebra 72: The finite field of size p, where p is a prime

Abstract Algebra 72: The finite field of size p, where p is a prime

Abstract: We give an introduction to the finite field of size p, where p is a prime. Recall that Z/pZ={0,1,2,...p-1} is an abelian group under addition modulo p, and that if you remove zero then you get the abelian group of units U(p)={1,2,...,p-1} under multiplication modulo p. We use the fact that p is prime when note that U(p) contains all of the numbers from 1 up to p-1. Indeed, if n is not prime, then U(n) does not contain all of the numbers from 1 up to n-1, but instead only those numbers that are relatively prime to n.

This video accompanies the class "Introduction to Abstract Algebra" at Colorado State University: