Coherence invariant maps on tensor products

In 1940s, Hua established the fundamental theorem of geometry of rectangular matrices which describes the general form of coherence invariant bijective maps on the space of all matrices of a given size. In 1955, Jacob generalized Hua's theorem to that on tensors of order two over division rings with more than two elements. We generalize Jacob's result to that on tensors of any finite order over arbitrary fields and use the result to derive a special case of a theorem on linear decomposable tensor preservers of Westwick in 1967.