Quillen's lemma

Let $𝐴$ be a $𝕂$ -monoid over $𝕂$ and $𝑉$ be a simple $𝐴$ -module. If $𝐴$ has a filtration ${𝐹 𝑖 𝐴} \infty 𝑖 = 1$ such that $1 \in 𝐹 0 𝐴$ and the associated graded algebra is a finitely-generated commutative $𝕂$ -algebra, then every $𝐴$ -module endomorphism $𝜗 \in 𝐴 𝖬 𝗈 𝖽 (𝑉, 𝑉)$ is an algebraic element over $𝕂$ .¹ #m/thm/module