In this question, all rings are commutative with a $1$, unless we explicitly say so, and all morphisms of rings send $1$ to $1$.

Let $A$ be a Noetherian local integral domain. Let $T$ be a non-zero $A$-algebra which, as an A-module, is finitely-generated and torsion-free.

Can one realise $T$ as a subring of the (not necessarily commutative) ring $End_A(A^n)$ for some $n \ge 1$?