Riesz representation theorem on generalized n-inner product spaces

In this paper we develop a generalization of Riesz representationtheorem on generalized n-inner product spaces. We show that any alternatingn-linear functional on a finitely generated standard generalizedn-inner product space can be represented by a finite number ofn-tuples of vectors. The proof of the theorem utilizes an inner producton a quotient tensor product space induced by the generalized n-innerproduct.