Abstract Algebra | The field of fractions of an integral domain.

We present the notion of the field of fractions of an arbitrary integral domain, give some examples, and prove that we indeed have constructed the smallest field containing the original integral domain.
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[@AKhoja]

Hey Michael, I really love your videos. I noticed that you cover a very broad range of topics on this channel, which is cool, but have you considered working on more chronological series that cover the foundations of different subjects in math? I would love to see, for example, a series building abstract algebra up from the ground, or seeing a series on the Zeta function and its properties in number theory. Maybe that's not the sort of content you'd be interested to make, but I thought it would be nice to suggest.

[@MichaelPennMath]

All of the videos that are titled in the form Subject Name | Topic are part of course materials that I put together for my teaching purposes. As such, most of them are part of big playlists that are more or less in order and start at the very beginning. For example, here is the full Abstract Algebra playlist:
ruclips.net/p/PL22w63XsKjqxaZ-v5N4AprggFkQXgkNoP

[@AKhoja]

@@MichaelPennMath The playlist section on your channel is so extensive that I didn't spot them! Thank you

[@ImaginaryMdA]

This is lovely, and a great way to show that the field of rational polynomials is in fact a field, IMO. Doesn't require any fiddley details.

[@niklasnetter2190]

Just great! The speed is just perfect.

[@ojas3464]

It appears we only need that the Domain be commutative and cancelative, and the existence of multiplicative inverse could be waived. By defining the inverse image of the Diagonal of D X D of the imbedding map into the Quotient Field, a multiplicative identity for D could extracted, disregarding Set-Theoretic issues

[@jackmaibach8316]

Great content as always!

[@xshortguy]

That awkward moment where the video is not well defined when proving that the field of fractions addition is well defined.

[@johnkevinpadro7819]

Hi Sir Michael, can you discuss about Algebraic Extensions of a Field??

[@bishwajitsarma5768]

Which part proofs the uniqueness of the field of fraction?

[@natepolidoro4565]

Chek

[@vadimpavlov6037]

Jumpscare at 0:08

[@kushagrasinghal8209]

gg