Jose Brox

(I mean I don't think this is a feature of the chatroom, but an external program made on the part of the interested person)

@rschwieb I'm not sure how this is done. I guess it is a little program with HTML code. Perhaps you can ask this in META (or ask directly to the person doing it with XKCD!)

Btw, in the new DaRT addition I see an extraneous slant bar "/" next to the ring of integers

I'm keen to see the new updating scheme

@rschwieb Glad to see the DaRT growing :) :)

I don't know about Atom, I figure it never was as popular as RSS, so it should have had only moderate success (as always happens when two technologies fight for some market niche, even if the second one is better) and should also be dead/dying by now (what I see in Wikipedia is that its last version comes from 2007 !!)

Can't you get some predefined template to do the opt-in? In some places you just tick a box saying "I want to stay updated on this" and introduce an email. The Wordpress idea is cool, I receive some updates from it (as Terry Tao's "What's new?" new posts).

@rschwieb Yes, all subscriptions I have by now to updates in webpages I'm interested in come to me through email, which happened quite naturally (and gmail is a good enough mail server for me, with labelling, etc.). The last thing I ever had by RSS was a Lie algebras journal page (I tended to forget to look at it) and finally I replaced the RSS by a button on my browser's toolbar :P.

(Btw, I see those numbers and articles as a point in a dynamic set whose evolution shows a clear trend, as happens with technologies in society)

Well, I'm convinced as a telecommunications engineer and a techie. 23 million sites still use it, but what about the number of users? What I did once through RSS, today I do through email. Perhaps you could think of some kind of mailing updates?

Moreover, rss is going to be discontinued soon, at least in Firefox

The best way I can think of in order to broadcast requests is actually to write questions about them on Math.StackExchange :D

It is exercise 6.23

@rschwieb Hi again! It is done!

Kindest regards! :)

I'll leave for now. My connection problems are really killing me... but you can write anything in here and I will read it later, or you can write to me at [email protected] if you prefer

I think I would maintain the same page, and distinguish the properties by the characteristic, as in Simple: yes (char 0) / no (char p)

@rschwieb On the other hand, I don't understand why in the DaRT definition for the Weyl algebra you have K to be countably infinite

Sorry, this room is for other subjects! I'm not really free now. Can you write me an email?

Hi, maths student!

I mean that Weyl algebras as you have them defined (well, you get x1,...,xn and y1,...,yn where yi is the derivative of xi) are isomorphic to differential polynomial rings (with the usual derivative as the twisting derivation), but I'm not sure if this is true anymore in char p. In a quick look, they seem to be the same, but...

Domains yes, because you have the degree

I don't think you will have them disguised. Weyl algebras are differential polynomial rings, but I'm not sure if they are still in char p or not. There is yet another definition, but I don't recall it now

So A is not simple

You see, if char(K)=p, then [y,x^p]=px^(p-1)=0, so x^p commutes with y, but also with x, hence with the whole algebra A. Then the ideal generated by x^p is just x^pA, and x is not in there due to degree, that can be defined in this context also

Sorry: all definitions agree in char 0, but do not in char p. In char p, some are simple and some are not

Let me check my notes

The problem is with the alternative definitions (some are simple in char 0 and some are not, for example)

I'm thinking about it. The PI part would be no problem because Kaplansky's theorem goes well for all rings and for all PIs (not just multilinear)

@rschwieb Nice to know you better too! If you are into Python, do you use Sagemath much?

:49500024

Sure, he was strong and creative! Also Amitsur, that I feel is not well enough. He may be even better than Kaplansky!

I'm experiencing internet problems, do you copy me?

He noticed that Hall's identity in division rings forced them to be fd algebras, and asked "what more can be said"?

Yes; in fact, that was the main idea behind the original development of PI theory by Kaplansky

The original paper of Kaplansky is Rings with a polynomial identity (1948). The theorem is in all serious books about PI rings. For example, in Rowen's Polynomial identities in ring theory it is Theorem 1.5.16

Hi again! Sorry, my wifi router has to be reset from time to time

Yes, give me a second

I see! I graduated in 2008 but did not doctorate until 2015 (previously I studied telecommunications). I'm a postdoc these days

I'll be on guard and try to contribute to DaRT. I am myself bad for remembering properties...

I'm glad for you and your son! I thought you were "older", taking into account the level of your contributions

I think you don't have Weyl algebras in $2n$ variables, but don't know if they count. Besides, in positive characteristic there are differing definitions of Weyl algebras

Oh, congratulations! Is all going well with him/her?

Perhaps two weeks? I don't know, time goes weird around me :P

Yes, of course! But ideally, I'd like many more rings to be there!

(I think I made the suggestion like one month ago or so)

Haha, thank you! But in this case it is simple enough to check for yourself, I believe!

Ok! I saw it was still pending, and wondered...