5 problems

Let $A$ be a finite-dimensional non-selfinjective algebra, and let $n$ be the number of simple $A$-modules. The dominant dimension of $A$ is denoted by $\operatorname{domdim}(A)$.…

Let $K$ be a field, let $S_R(n,d)$ denote the Schur algebra over a commutative ring $R$, and let $V$ be its natural module. For $n,d\in\mathbb{N}$, write…

Dominant-dimension property conjecture. Every finite dimensional algebra with finite dominant dimension $n\geq 1$ has property $*$.

Dominant-dimension conjecture. The algebra $B$ has dominant dimension $n$.

Abrar's conjecture.