2 problems

Let $V_1=V(a)\oplus V(b)$ and $V_2=V(c)\oplus V(d)$ be the socle decompositions of two uniserial $\mathfrak{sl}(2)\ltimes V(m)$-modules, as in the classification theorem, and assum…

Let $\Lambda$ be a triangular algebra and let $U$ be a uniserial $\Lambda$-module with mast $p$. Write $J$ for the Jacobson radical, and let $B$, $C$, and $D$ denote the sets of ar…