2 problems

Let $A$ be a finite-dimensional algebra over a field $k$. Write $\operatorname{brick}(A,d)$ for the set of isomorphism classes of bricks of dimension $d$, and call $A$ brick-finite…

Let $k$ be a commutative artinian ring, $A$ an Artin $k$-algebra, and let $\operatorname{mod} A$ denote the category of finite length left $A$-modules. Assume that…