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>=1?