Abstract Algebra | Introduction to Unique Factorization Domains

[@Thegeektoendallgeeks]

shouldnt the result of (1+sqrt(5))(a+b*sqrt(5)) = (a+5b) + (b + a)sqrt(5) regardless as a result you would get b = -a ---> -4a = 2 --> a = -1/2 which is not an integer leading to the same conclusion that u is not in Z[sqrt(5)]

[@ezraguerrero2879]

Yes, he had a typo that luckily did not alter the result.

[@asht750]

can you add more abstract algebra videos on modules and fields? Module theory and field theory with Galois theory?

[@frankreashore]

Nice. I liked your counter examples.

[@addemfrench]

At about 7:00 I think you're saying that if a=/=0 then b=0. Not clear to me why. Maybe something like: a^2+3b^2 is a large positive number so we need to minimize it if this is going to divide `a`?

[@timurpryadilin8830]

Can you make a video about a proof of the Fermat's Last Theorem for cases n=3,4,5? For n=4 it is quite trivial, and for n=3,5 it requires some ring algebra, but I am sure you can present it easily

[@MichaelPennMath]

I already have an n=4 video!! kzbin.info/www/bejne/aHrOhWdomcZkmJo I will put those other cases "on the list".

[@timurpryadilin8830]

Thank you! I am looking forward for tge other cases! By the way, do you have any understanding of the the Andrew Wiles's proof or at least the theory of elliptic curves? I want to learn them on some minimal level an perhaps you could make a video about them too

[@firettoYT]

In your definition of irreducible, you forgot to state that an irreducible element cannot be a unit.

[@heisenbergmuzik4948]

I think there is some misunderstanding. Plz clarify. a/a^2+3b^2 would belong to Z only for a=0 coz a,b belongs to Z.

[@asht750]

Yes, I agree. Something is off