Abstract Algebra | Constructing a field of order 4.

We use the standard strategy involving a quotient of the polynomial ring Z2[x] by a maximal ideal in order to construct a field of order 4.

[josh]

Also note that the finite field of order 4 is NOT isomorphic to the integers mod 4. That's a somewhat common misconception.

[davidescobar]

Fantastic channel ... I don't know how I could have missed this type of content on this platform. Many thanks Professor. Greetings

[paul]

At 5:58 Z alpha (alpha) is actually Z2 (alpha)

[vanessamichaels]

why is 2x^2=0?
why are you screaming?

[jordancourtemanche]

Since you're in characteristic 2, another cool way to calculate (α+1)(α+1) is through the Frobenius map.

I've really been enjoying your content, especially since you go in so many different interesting directions. And you've been on a tear, putting out new videos!

[tLearningTree]

I don't get the part at 3:18 - 3:55 . Can someone explain to me?

[howardcheung]

Sir can u make some more videos on finite field?

[عادلبناصر-غن]

من فضلك أريد حل تمارين عملية في حقول ومجموعات👍👍👍👍👍👍

[kevinsuryapranata]

Very nice explanation, I really thanks for this video Sir.

[mac]

I've rarely ever had less doubt that someone completely understands something...

[عادلبناصر-غن]

thank you sir Please I want to solve practical exercises in fields and groups

[mark_tilltill]

Take the product and use synthetic division keep the remainder.

[cameronspalding]

I heard that every finite field has a size that is prime or a power of a prime
I could understand fields of prime order: Zp where p is prime, but I couldn’t understand fields with job prime order

[Jim-vrlx]

Can someone help explain why AES, in GF(2^8), uses the irreducible polynomial x^8 + x^4 + x^3 + x +1 while the Twofish algorithm, in GF(2^8), uses a different irreducible polynomial x^8 +x^6 +x^3 +x^2 +1 ? Wont both polynomials produce the same values if there is only one finite field of order 2^8? I was told never to mix polynomials -- pick one polynomial and stick with it.

[maxamedaxmedn]

I think i can't understand this type of math