Integral Domains (Abstract Algebra)

Integral Domains are essentially rings without any zero divisors. These are useful structures because zero divisors can cause all sorts of problems. They complicate the process of solving equations, prevent you from cancelling common factors in an equation, etc.

In this lesson we introduce the idea of an integral domain, talk about solving an equation over rings with and without zero divisors, and show how the cancellation property does hold in an integral domain.

Be sure to subscribe so you don't miss new lessons from Socratica:

♦♦♦♦♦♦♦♦♦♦

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

Milne, Algebra Course Notes (available free online)

♦♦♦♦♦♦♦♦♦♦

Ways to support our channel:

► We also accept Bitcoin @ 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9

Thank you!

♦♦♦♦♦♦♦♦♦♦

Connect with us!

♦♦♦♦♦♦♦♦♦♦

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

♦♦♦♦♦♦♦♦♦♦

[derendohoda]

Whoever wrote the scripts for this playlist did an absolutely outstanding job.

[PunmasterSTP]

I think this lecture is very well grounded; it’s got a lot of roots! In all seriousness, this is another phenomenal video, and I do plan on binge-watching the rest of the abstract algebra playlist today.

[jonathanpopham]

I was reading a book on abstract algebra that explained integral domains and it completely left out the part about the usage of modular arithmetic. Totally didn't understand. This makes it very clear, thank you.

[codatheseus]

They were talking about zero divisors in my linear algebra course and it makes so much more sense now after this video

I'd love to have a socratica video series about dual numbers

[johnfisher]

Why does abstract algebra seem so much simpler this way? Love this. Maybe you could add one on the definition of an algebra.

[PearlKhurana]

I always revisit the series before any of my abstract algebra papers for basic definition clarity! Would love to see more being uploaded. Kudos to the author!

[somadityasantra]

Your channel deserves a lot more attention.

[jordanweir]

These are all wonderful videos, brilliantly narrated, keep up the good work

[rajkumarmukherjee]

You are my all time favourite Teacher.

[turalsadigov]

Just great! I just discovered your videos, and it is fun to watch them!

[danielholme]

Liliana, these videos are so good, compressing down the succinct core knowledge on a topic into a few minutes, just what's needed to dip in and update as required.

[ChaudharyAteeq]

Thanks for adding a new video about Abstract Algebra...Plz upload more videos on Pure Mathematics...
Your explanation technique is great...

[theboombody]

The video is good throughout, but the end part alone is worth a thumbs up.

[andresvalera]

Good explanation !, The book my university gave me just says "It's a ring in which a.b=0 implies that either a or b is zero" which is true but misses the whole point of defining a structure smh


Also wanted to add that in some books "The integers mod n" are noted as Zn (The n being a subscript)

[tomhu]

Really best video for abstract algebra: the instructor explains clearly in reasoning

[akarshroy]

Love your way of explanation from India Ma'am . 👍🏻

[Dannnniel]

this is like the 5th of your vids so far, thanks for helping me pass my algebra exam :D

[avishekadhikari]

Innovative lectures I liked it so much

[harshagrawal-ez]

THANK YOU .GOT TO LEARN ALOT OF NEW THINGS

[ndubuisiuguru]

This is quite clear and easy to understand.