Abstract Algebra | Introduction to Unique Factorization Domains

We introduce the notion of a unique factorization domain (UFD), give some examples and non-examples, and prove some basic results.

[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)]

[asht]

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

[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`?

[timurpryadilin]

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

[heisenbergmuzik]

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.

[firettoYT]

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