# Tag Info

1 vote

### A result of Schofield in the case of quivers with relations

The question doesn't seem to be a generalization of Schofield's result (which doesn't involve fixing a brick $B$), and seems to be false already for quivers without relations. Take $Q$ to be the ...
1 vote
Accepted

### Automorphisms of special egg-box diagrams

It turns out (surprisingly) that the answer to my question is yes, and there are even finite examples. I came up with the following diagram  \begin{array}{|c|c|c|c|c|c|} \hline \circ & \circ &...

### Subrings, submodules, and flatness

No it need not be an isomorphism. Something more than flatness is required. For example, taking $M$ and $N$ to be copies of the ring $R$ you are asking for the multiplication $R\otimes_SR\to R$ to be ...

### Is any finite-dimensional algebra a sub-algebra of a finite-group algebra?

Assuming that by "sub-algebra" you mean "unital sub-algebra": Every group algebra has a one-dimensional module (the trivial module), so any subalgebra has a one-dimensional module. ...
Accepted

### Distributive lattice of subspaces

Just to not leave this open, a proof can be found in Proposition 7.1 of Chapter 1 of Quadratic Algebras by Alexander Polishchuk and Leonid Positselski as alluded to by Mariano on MSE https://math....

### An example of a local integral domain with special spectrum

Put $D_0 = \mathbb{Q}[T,X_1,X_2,\cdots]/I_0$, where $I_0$ is generated by the elements $X_i^2-TX_{i+1}$, for every $i \in \mathbb{N}$. This is a domain. Let $\mathfrak{m}_0$ $=$ $(T,X_1,X_2,\cdots)$, ...
Let $k$ be a field. Put $R=k[[x,y]]$ and let $D\subset R$ be the subring $k+xR$. It consists of power series without any term $ay^n$ ($a\in k^\times$, $n>0$), or (equivalently) series $f(x,y)$ such ...