Recall the ring of polynomials $R = F[t]$ with coefficients in a field $F$.
Fix $T$ in $\mathrm{Hom}_F(V,V)$. Show that there is a unique (left) $R$-module structure on $V$ such that
$(a + bt, v) = av + bTv,$ for all $a$ and $b$ in $F$.
Hello. I'm having trouble with this homework problem. Particularly, I don't exactly understand the relationship between $t$ and $T$. Could someone please explain to me what this question is asking?
Thanks, Natasha