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

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

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

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

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

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....🙏

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

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

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

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

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.

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

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 #

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

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).

I love all this videos. This is the kind of math that I really enjoy and it's explained in an excellent way.

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

Love this series!

This was fantastic! Thank you so much!!!! I think you may save me this semester

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

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).

Beautiful videos. One cannot avoid falling in love with math.

Muito bom! Continue com essas lições! Obrigado!

Indeed fantastic series!

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

your videos are absolutely fabulous..

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

Your lecture is so helpful mam!

Incredible, way of teaching Thankyou so much

Thank you so much.

Lec are so simple every one can understand easily thank u for making videos

very helpful. Thank you

Ma'am you are an icon and a legend. Thank you !!

Love your content !

What a brilliant explaining 😊

Thank you for best in world classes 😃

Great videos!

Can you please do more videos on congruence arithmetic including the euclidean algorithm?

Great video!!!

Great work

your teaching technique is so good i like it .thanks❤❤❤❤👍👍

6:27 Wedderburn's Theorem: there are no finite noncommutative division rings (rings all of whose nonzero elements have multiplicative inverses). But finite noncommutative non-division rings: matrices over a Z/n with n composite might work.

your lectures are amazing maa'm

I like how the background theme song changed when you start introducing the fields :)

Example of a finite noncommutative ring, maybe The set of 2x2 Matrices where the entries are from The integers mod n (Z/nZ)

it's awsome explanation mam......

The quotient group Z/nZ should be Z/nZ = { [0], [1], [2],..., [n-1] }, where [a] = a + nZ is an equivalence class.

So, we need a finite set of elements and matrix. We can limited a set by using { module, char, int, etc in computer science, other set } Is there a way for not using matrix?

One of my best teacher ..Socratica . Love from pakistan .. keeping it up ,so that we learn easly ..🇵🇰🇵🇰

Really it's understandable. Tq mam.

Nice one

So many questions I had explained in under 8 minutes

I paypaled $20, ♥💕 your content.

Thank you

Really nice

An example of a finite non commutative ring is the set of matrices with elements in Z3

thank u very much mam ...

Thanks for the video, How can i find the inverse of (1,2) over the ring R = Z5?

Mam pls make a video on ideal rings

Like the shirt like nice color hoping to see some division ring examples too cuz vector spaces right ▶️

Very useful

Don't worry I have already joined the fellowship of the Ring😆 since childhood, thank you for your wonderful explanation...

Great video as always, but a ring A can existe without identity element "1_A" ? because when I read the definitions given on french website and in my french course, the present of 1_A an identity element is required, same for sub-rings

My answer for the final question would be a ring consisting of the 2x2 matrices where all the elements of the matrix are the integers mod n. The ring would be commutative under addition from the definition of a matrix and because the integers mod n also being commutative. And of course matrix multiplication is non-commutative. Am I right?

madam please send a video on ideals

Thanks

In fact, every ring is a group, and every field is a ring. A ring is a group with an additional operation, where the second operation is associative and the distributive properties make the two operations "compatible". A field is a ring such that the second operation also satisfies all the group properties (after throwing out the additive identity); i.e. it has multiplicative inverses, multiplicative identity, and is commutative. In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra. It consists of a set equipped with two binary operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects such as polynomials, series, matrices and functions. A ring is an abelian group with a second binary operation that is associative, is distributive over the abelian group operation, and has an identity element (this last property is not required by some authors, see § Notes on the definition). By extension from the integers, the abelian group operation is called addition and the second binary operation is called multiplication.

A ring is an abelian group and a monoid such that the monoid operation distributes over the group operation

Wonderful.. ❤️❤️❤️

I CAN LEARN ABSTRACT ALGEBRA ONLY FROM SOCRATICA. THANK YOU SO MUCH SOCRATICA.

This video is well done I’m studying for my math teacher’s exam in California that I’m taking in 12 hours

Fantastic

Unit quaternions with integer coefficients.

Good video

thank you madam...........

thanx for giving knowledge. from which country you belong kindly tell me i really impress from your lectures

N->regular set Z->(commutative) ring Q->field R->field C->field

I love you too much u just saved me

Please describe division ring

A non commutative finite ring is set of matriex whoes elements is from Z/nZ ( for every n is element of Z)

Hmm, finite noncommutative ring? What about ring of matrices whose elements are from set Z/nZ?

reallyy mam.. u r suprb..😄😄..

5:35 if the integers mod (some prime) is a field, wouldn't that require there to be a multiplicative inverse for 0?

Excellent.I want the videos on Linear Algebra is it possible

Please give me video of product of two rings

Proud to join the fellowship of the ring

I learned all about algebra and what my Ma'am wants to tell. Thanks

Just for the fellowship of the ring, I give 2 thumbs up!!!!

Once we have established the definitions of various types of ring, is there anything else that can be said about them. Do all commutative finite rings have some property in common. If so, what is it? If not, what is the point of all this?

In integer mod n ring how can we check inverse w.r.t addition property?

05:12 Can you talk some more about those ideals? I don't see them being introduced anywhere on this playlist. 06:46 Dying inside a little bit when reading that from the prompter there, eh? :) OK, I guess that the 2×2 matrices with coefficients being integers mod n is the non-commutative finite ring we're looking for?

how to find cayley table is associative

Mam you help to solve some problem in ring theory?????

Set of all nxn matrices over a finite field whose bootom row is zero is a finite non commutative ring

Plz....explain mam The set of all continuous real-valued functions of a real variable whose graphs pass through the point (1,0) is a commutative ring without unity without unity under the operations of pointwise addition and multiplication, i.e., the operations (f+g)(a) = f(a)+g(a) and (fg)(a)=f(a)g(a)

Awesome mam

Any chance of getting to algebraic topology?

Estou de queixo caido com voce Liliana Castro !!!!!!

Thanks!