Ring Examples (Abstract Algebra) 

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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.

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

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....🙏

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

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

I paypaled $20, ♥💕 your content.

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).

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

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 #

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

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

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

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

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

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

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

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

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 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).

Im going into 8th grade. Will someone explain what's going on...im being serious I'm going to have to take it back.

identity crisis fellowship of the rings P.S.: I love you so much for excavating the fun in math.

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

"...join the fellowship of the ring..." Aaaughhh! Math joke! Math joke! Got a chuckle out of me, though so kudos.

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

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

Zahlen is plural: numbers. Ja wohl!

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?

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.

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

Hi, can you make a video of Tensiorial Calculus ? Because is complex as Abstract Algebra 🥵

More intelligent and brave women like you please 🥰 Science would be so much better than 🎉🎉

Q1.every non zero commmutative ring R cotains maximal ideal Q2.Show that a ring R is the zero ring i.e R={0} ⇔ 1=0

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

These are not examples as I define them. Instead, proffer a "word" problem or proof where rings would provide the most direct method to solve or prove.

I'm a big fan of your videos but this video was hastily motivated and rushed.

how will the elements in z/3z be = (0,1,2) ? Can someone plz help

A finite non-commutative ring would be a matrix with integers mod-n?

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

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

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

Socratica: you rock!!! If I was stinky rich, you would all have a good salary. Unfortunately, I am a poor physics teacher, and I will give you 20 euros.

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

Poor 2 x 2 matrix: “I may not commute, but at least I have an identity!”

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.

What.is.going.on.

I like its video

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

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

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

Any one tell me how finite non commutative ring is combine ?example?

Show that if R is commutative then R[x]is also commutative.

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

5:59 The ADDITIVE structure of rings is a group: an abelian group, specifically. But, don't say rings, in general, are a subset of all groups. In general the multiplicative structure on rings is not a group.

in the integers mod 3 consider the matrix A= ( 1 2 and B=(1 1 then A times B is not the same as B times A 0 2) 1 1)

This poor ring is having an identity crisis." Great pun.

Every subring of integer is an ideal...????

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)

You sad for real polynomials multiplication is commutative but why isn't same for complex polynomials. Any counter example.

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

like for the identity crysis joke :D hahhaa

Proud to join the fellowship of the ring

madam please send a video on ideals

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?

Nice, digestible videos overall. I disagree with the Venn diagram however. It makes no sense to say that the set of rings is contained in the set of groups. Given an element R from the set of rings, R is not in the set of groups since R has 2 binary operations. You can say that, given a ring, (R,+,x), (R,+) is a group. To extend the argument, you would not say that the set of groups is contained in the set of sets, because a group has a binary operation, and sets do not.

I didn't know you could do so many things with polynomials. Or should I say, poly-know-more-ials? 😎

Muito bom! Continue com essas lições! Obrigado!

A matrix describing vectors on a spherical surface is a ring of finite mod n elements. There, I am now a member of the Fellowship Of The Ring

Mathématiciens do often start with groups, but computer scientists often start with monoids. Monoids are like group, bit operations are often not invertible.

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

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

The lord of the ring reference is sending me :)

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?

How to prove that (N,+,*) is not field in linear algebra? Can u plz tell me solution.

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

i was invited to tour with Hopsin, but because i dont have a car to go to Hamburg, i couldn't show up...

Incredible, way of teaching Thankyou so much

I just sent you 100 euro ..lol just kidding. But u r very good teacher. not kidding

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

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

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?

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

honestly your explanations are detailed but too difficult to understand

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

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

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

Not all fields are commutative, for example the field of Hamilton.

R={(a b) :a ,b€Z } what's type of ring is this ?

Why are you just so amazing and great in teaching this! What's her name by the way

Wonderful.. ❤️❤️❤️

The music just adds to the abstraction of this field of math..

If I get a big grade ( >7 ) in my Algebra exam, I’ll donate

Thanks define the elements of the matrix to Z/nZ feel free to debate or correct me

So many questions I had explained in under 8 minutes

I love you too much u just saved me

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

Identity crisis? 🙄❤️

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