2 problems

Let $n$ be a positive integer, and let $\mathbb{M}_{n}(\mathbb{F}_{2})$ denote the ring of $n\times n$ matrices over the field with two elements. An idempotent is an element $e$ sa…

Let $R$ be a ring. Its right injective profile $i\mathcal{P}(R)$ is the lattice of classes of right $R$-modules of the form $\operatorname{\mathfrak{In}}^{-1}(M)$ for some right…