0
votes
1answer
39 views

Lie rings: reference request

Dear friends: I am looking for a modern reference for Lie rings (In particular, I would like to have nice references for the structure of Lie ideals), let it be lecture notes or a book, in the sense ...
3
votes
1answer
61 views

Books on Rings without Identity

I was just wondering if anybody knows of any good books or articles that study rings (and algebras) without (or not necessarily with) identity. I have gone through Thomas Hungerford's $Algebra$ ...
3
votes
0answers
20 views

Reference for proof of homotopy invarance of Cyclic cohomolgy

I'm looking for a good reference for a proof of the homotopy invariance of cyclic (co)homology. I'm following a refernce book by Joachim Cuntz, the proofs are ommited therein, or only shown in the ...
16
votes
1answer
203 views

How 'commutative' can a non-commutative ring be?

Let $R$ be a finite non-commutative ring. Let $P(R)$ be the probability that two elements chosen uniformly at random commute with each other. Consider the value $$S=\sup_RP(R)$$ where the supremum ...
1
vote
1answer
98 views

Name of $a*b=c$ and $b*a=-c$

$A_+=(A,+,0,-)$ is a noncommutative group where inverse elements are $-a$ $A_*=(A,*)$ is not associative and is not commutative $\mathbf A=(A,+,*)$ is a structure where 1) if $a*b=c$ then $b*a=-c$ ...
6
votes
0answers
205 views

When is $\mathbb{Z}\Gamma$ a left Noetherian ring?

Denote $\Gamma$ to be a countable discrete group, let $\mathbb{Z}\Gamma$ to be its integer group ring. A ring is left-Noetherian if it satisfies the ascending chain condition on left ideals.(c.f. ...
3
votes
1answer
59 views

Center of a quantum matrix algebra

Let $p \in k^\times$ be a nonroot of unity. It seems to be a well-known fact that the center of the quantum matrix algebra $\mathcal{O}_p(M_n(k))$ is generated by the quantum determinant $D_p$. It is ...
3
votes
2answers
328 views

Wedderburn-Artin theorem

There is a website with a short proof of Wedderburn-Artin theorem link. I am not sure if the proof is ok and in fact I haven't understood what the following lemma means: Lemma 1. If $M$ is a cyclic ...
3
votes
1answer
179 views

Cyclic Algebras over local fields- reference request

I am looking for an introductory text to the subject of Cyclic Algebras, and in particular ones defined over a local field. A cyclic Algebra, to the best of by understanding is defined as follows: ...
2
votes
1answer
209 views

Relaxing the definition of a von Neumann regular ring

Hereinafter, all rings are assumed to be unital but not necessarily commutative. A well-known class of rings are von Neumann regular rings, that is, rings $R$ such that for each $a\in R$ there is an ...
6
votes
2answers
241 views

Example of a commutative perfect ring that is not artinian

I read a result here stating that a commutative perfect ring is artinian if and only if it is $(1,1)$-coherent (see Proposition 5.3). I'm interested in finding an example of a commutative perfect ...
6
votes
1answer
527 views

Supplementary exercises for Herstein's Noncommutative Rings

I've been studying from the book Noncommutative Rings by Herstein (not as a part of some official course), but unfortunately it doesn't contain any exercises apart from a few simple ones in the body. ...