A note on algebraic automorphisms (Q805675)

Let V be a vector space over the field k and let t be an automorphism of V. Assume that t is algebraic with minimal polynomial P(T)\(\in k[T]\). Let k(V) be the field of quotients of the symmetric k-algebra of V and let s be the k-automorphism on k(V) induced by t. The authors show that s is completely determined by P(T) and \(\dim_ k(V)\).