RNT2.3. Euclidean Domains

Ring Theory: We define Euclidean domains as integral domains with a division algorithm. We show that euclidean domains are PIDs and UFDs, and that Euclidean domains allow for the Euclidean algorithm and Bezout's Identity.

[slowfreq]

My professor doesn't speak English, so this was very helpful!

[MathDoctorBob]

You're welcome, and thanks for the kind words!

[BareClause]

Fun fact about Euclidean domains, the only Euclidean domain with uniqueness on the pairs q and r are fields and polynomials rings over a field.

[Ilovecalculus]

your videos are explained in a very organised manner. thanks a lot for putting these videos on you tube.

[gustavogordillo]

Thanks. I learned and understood su much more watching this video.

[muhammadsajjad]

Is Eisenstein integers a euclidean domain?

[AlonAshkenazi]

Thank you very much! It's all clear now!
Your videos get me through my degree :)

[brunorocha]

Hey man. Your videos are great and very didatic and instructive. Greetings!
But, during the proof about Euclidean Domain be a PID, you got b in I s.t. d(b) is the smallest. And then you said that we can't pick an r in R s.t. d(r) < d(b) 'cause the nature of b. But b is the element of I s.t. d(b) is smallest. So, should we show that r belongs to I to ensure that we can't pick s.t. d(r) < d(b)? Or I am wrong?
Thanks!

P.S.: Sorry for my bad English... :D

[MathDoctorBob]

You're welcome, and glad to be of help! Ay! Your teachers are getting paid to do that.