Does anyone know anything about the normal regular sequences in the quantum plane? Here are the definitions: Normal regular sequence: Let $R$ be a ring (not necessarily commuta …

Let $R$ be an associative and non-unital ring. (Suppose that $R$ is $s$-unital, i.e. for each $x\in R$ there is $u,v\in R$ such that $ux=xv=x$.) It is not difficult to show that i …

I asked this question on SE a long time ago, but never received an answer: The Govorov-Lazard Theorem states that a (left) module over an unital ring is flat iff it is a direct l …

Given a Lie algebra g, with $Ug$ being its universal enveloping algebra, one can construct a cochain complex $d: Ug^n \rightarrow Ug^{n+1}$, and a Gerstenhaber brackt on $\oplus …

I'm interested in Sklyanin Algebras or Artin-Shelter regular algebras of type A. These are generated in degree 1 by three variables x,y,z, and have three defining relations in deg …

Definition: a (not necessarily commutative) left and right Noetherian ring $R$ is said to be Auslander-Gorenstein if (i) $R$ has finite left and right injective dimension (in whic …

While analyzing convergence speed of stochastic-gradient methods for convex optimization problems, Recht et al (2011) posed a tantalizing conjecture. It seems quite tricky, so afte …

I'm interested in knowing/collecting some properties of epimorphisms of rings (with identity) that are true over commutative rings but are false in the non-commutative case. Examp …

Can anyone help to find some information about these structures?

By inspecting the accepted answer to this question http://mathoverflow.net/questions/120918/are-epimorphisms-from-a-division-ring-isomorphisms one obtains the following necessar …

Definition and context: An (associative, unital, not necessarily commutative) ring $R$ is called classical if every regular element of $R$ is a unit. Equivalently, $R$ is its own …

According to Corollary 1.2(3) of the paper Silver: Noncommutative Localizations and Applications. J. of Alg. 7(1964), 44-67: If $R$ is a (commutative) field and $\alpha: R \to …

If $G$ is a profinite group, then the category $Mod(G)$ of discrete $G$-modules has sufficiently many injectives (Neukirch, Schmidt, Wingberg: Cohomology of Number Fields, 2.6.5). …

I was reading Hodges' "Model Theory" Chapter 8 a propos existentially closed models of $\forall_2$ theories in a countable first order language $L$. He extends the proof of the om …

For an ideal $I$ of a ring $R$ with identity, let $r(I)=\{r\in R: Ir=0\}$ and $l(I)=\{r\in R: rI=0\}$. Question: If for any two ideals (two-sided ideal) $I, J$ of $R$, we have $l( …