Not all finite fields are cyclic additive groups. Definition of characteristic, proof that all finite fields have prime power order, and explicit constructions.
Nice video - well presented. Been trying to find some down to earth explanation for this stuff for ages
jezza
Constructing finite fields? More like "Cool videos, and much knowledge they yield!" 👍
Also, did you mean to keep some of the videos in this playlist hidden? Out of the 36 videos, 10 are hidden, and it seems this wasn't meant to be the last video in the course. If it's not too much trouble, would you mind unhiding the other videos, or at least, pointing us to the next set of videos? Thanks in advance!
PunmasterSTP
You can have an infinite field with prime characteristic, for example the algebraic closure of any finite field.
terryendicott
thanx for explanation
I want to the name of the reference
Does anyone know the name of the book ?? plz
o-miraf
WTF ! - where is the rest of the course ? Gauss's Lemma / Eisenstein's Criterion and finishing conclusion of non solvability by radicals of the quantic / S5 / A5 ?
Hythloday
Incorrect on the characteristic of fields. Take the field of fractions of polynomials with coefficients in the integers modulo 2. Has characteristic 2 and is infinite.
connorjcelumba
05:19 LOL, I've seen one dude explaining this for half an hour :D
bonbonpony
1st 1/2 of the lecture is quite clear. second half is a lot incomprehensible. 1? Why is F a vector space over Zp? 2? why is |F| =P to the nth power? ....by thetenmnth of linear algebra? Sorry, but what are you talking about? Missing so serious explanations. I am frustrated
rhke
Wait why does every infinite fiel must have characteristic 0?
zairaner
Another very rough one to listen to due to the excessive lipsmacking, but good lecture otherwise.
