Ring Examples (Abstract Algebra)

Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more!

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We recommend the following textbooks:
Dummit & Foote, Abstract Algebra 3rd Edition

Milne, Algebra Course Notes (available free online)

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Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro
Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison
Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison

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[welovfree]

Thumb up if you want Socractica to do a playlist on: Number Theory, Topology, Linear Algebra ...etc

[digitsdigitsdigits]

"This poor ring is having an identity crisis."
You and me both, even-numbered matrix. You and me both.

[omgopet]

Come for the algebra lesson, stay for the puns. The delivery is amazing on both.

[yogitasingh]

An example of finite non-commutative ring is a finite MATRIX.
And the way of teaching is really very wonderful, I have learnt Group Theory from your videos in my previous college semester and now in this semester, you are again making it very easy to learn Ring Theory.
🙏🙏
Thanks a lot SOCRATICA🙏 for giving us an excellent teacher🙏....
Best wishes from INDIA....🙏

[swanhtet]

In this "Fellowship of the Ring" you are my lady Gandalf.

[fmagarik]

If you liked it then you should have put a group on it, such that it is abellian under addition, a monoid under multiplication and the distributive property holds

[__alex.grae__]

Love the video. One note from a German speaker: “Zahl” is number (singular), “Zahlen” is numbers (plural), “zahlen” is pay/paying (verb).

[Imakilla]

Literally laughed out loud when she said: "This poor ring is having an identity crisis". Think I've been studying too long...

[bablidas]

I never can forget the way u helped me.. These videos r really meant a lot to me... Thank u.

[sayy_gaarr]

That smirk at the end made my day!!! She was trying so hard not to laugh.

[Omnifarious]

Your bad puns, so carefully and thoughtfully delivered are amazing. I couldn't do better myself, and that's saying something (specifically, that I couldn't do better myself).

[Fematika]

Do the n x n matrices mod(n), meaning ((a mod(n), b mod(n)), (c mod(n), d mod(n))), with all of the usual operations, though each element is now mod(n).

[samcollins]

I loved this topic. I didn't know that rings existed in abstract algebra until now. I hope to see much move videos!

[amansingh-wwqc]

Amazing, with these small powerful videos filled with concept I learn everything

[sheepphic]

These are some of my favourite math videos! I've always wanted to learn abstract algebra, but it was always just a jumble of notation. Thanks for making these great videos to help people learn.

[zaidnadeem]

MASHALLAH.
THE WAY OF TEACHING IS VERY GOOD.
👍👍👍👍
MAY ALLAH BLESS YOU

[muh.khairulamtsal]

just found this channel, really intersting and decent way of teaching
love ur video sm

[oldPrince]

How to construct a finite non-comm ring.
If one uses the trick introduced in the video, one can take all 2 by 2 matrices whose entries only be 1 or 0. And addition/multiplication all usual matrix operations but under mod 2.
Then (01, 00)(01, 10)=(10, 00) but (01, 10)(01, 00)=(00, 01) hence non-comm.
Finite is obvious because we have 4 entries and each entry can be either 0 or 1 thus # <= 2^4 = 16.

[rcarnes]

Yep. I'm now a Patreon contributor. Excellent presentation.

[roadtofitness]

Mam your vedios are very helpful
Thanx a lot mam
Lots of well wishes from india