Відео

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HI, Professor. thank you for all the knowledge that you provide to us . your videos deserve millions views , you explain all good and in the easy way to understand. 10/10 👌

Great video, many thanks.

Great work... from deevige bangalore

@ZviRosen, can I email you some questions about one of your videos on commutative algebra. It has to do with ideal quotients.

For some reason, the proofs of many theorems in this lecture include even fewer details than those in Atiyah and Macdonald.

Can you share the lecture note?

What does it meant "specialize" here 26:55?

24:53 here A=R=any commutative ring, I guess?

Great lecture! But wait, Gauss' proof of the fundamental theorem is considered faulty? My day is ruined.

nice！

THANK YOU VERY MUCH PROFESSOR. Your lessons are very interesting 👍👍👍

Ohh, I see now why this very specific elements generate the submodule necessary to define the tensor product of the A-modules. How didn't I see that before. Thanks so much. Your explanation was very clear.

thanks a lot sir, master study is topolojy and now phd is algebra. so ıt was diffucult to understand such that flat modul. can ı get much more notes for flat module

Thank you so much for explaining it like this🙏

At 20:05, I’m not sure what it means 0 is not a closed point. Since the closure of {zero ideal} is not itself but Spec Z, set of zero ideal is not closed in Spec Z? Can you help to elaborate more?

Is localization only useful for algebraic reasons, or can we also get density and thus convergence? Lice real numbers can be seen as completion of the set of rationals, is there a similar concept for other sets of localized sets?

Very impressive lecture ... Please also make lectures on advanced group theory

Very good

How can we describe the submodules of S−1M over S−1A.

34:00 Why is it that 1-v0 has to be invertible for v0 in m?

Thank you for posting the videos!

Please do more topics on Dummit and foote.

There's a tiny mistake around 20:15; we should rather take y=-1 to get x, we get 2-x as is.

Hi Zvi, which software are you using to draw on the white board? I have not found any white board tool which really works well. They all either lag my hand or fail to draw smooth curves.

why do you define a "multiplicatively closed set". Why not simply say it is a "multiplicative monoid"? that already has 1, associativity, and closure. Right? associativity comes for free because it consists of elements from ring A. Right? Whenever I have a new definition for something that sounds awfully like something that already exists, I sweat wondering what is the subtle different that I'm not seeing. Are you claiming by avoiding the work "monoid" that you don't need associativity for some reason?

Your proof of Pascal's Theorem is incomplete. To assure that the conic F divides your polynomial g, you must assume that the conic is irreducible. Otherwise you can't guarantee that the entire conic divides the polynomial g. With this in mind, you can't prove the Pappus' Theorem based of the Pascal one, taking into account that the union of two lines forms a reducible conic (not an irreducible one).

can you give me the exercise of the tensor product of the module on a non - commmmutative ring .thank you

I was looking. For these thank you

Love how you used green pen for tropical semi ring

6:34 should there be I(X), not V(X)?

The example for D.C.C. is actually a special case of Prüfer group, the chain conditions are also studied in Hungerford's Algebra where he introduces these conditions on groups in order to prove Krull-Schmidt theorem :)

this is great

These lectures are great! Really appreciate it. And also I would like to share a math study message here for anyone who might be interested: I would like to read <Presentations of Groups> by D. L. Johnson. And I would like to ask if anyone is interested to read together? Because having a reading partner will make study more fun, especially when go through detail proof together. You are also welcome to share this message to anyone who is interested. Thank you so much!

Was really good to see how assuming a well-defined operation on the equivalence classes of the quotient necessitates that the [e] subgroup is normal. Thank you

Perfect pace and use of proofs. Superb lecturing!

Please post more lectures. Thank you

If [L:K] and [L:F] are finite [k:F] is finite from multiplicative property. For your proof of [K:F] finite how do you know the base vectors from [L:F] are in K, they might be in L-K?

Brilliant lecture

Really enjoying following along. Is there a syllabus for this course somewhere?

Nice, looking forward to following along :)

@13:27 what if one of the polynomials is monic, i.e. the ideal contains 1 ?

19:58 image of z in coker f' (not f)

@38:20 you mean sum of 'finitely' many cyclic modules ?

awesome class thank you :D

Super explanation sir, thank you so much sir

Good sir ge

Your lectures are great. Are you planning new series on homological algebra or algebraic geometry or representation theory etc And 28:10 what does it force to be an algebraic extension ? If not k[bar(x)] would be a ring instead of a field ? Is this the reason ? Thanks in advance

31:36 what you're saying is not what you're writing

Watching the whole series at 1,5 speed