Concrete two-set (module-like and algebra-like) algebraic structures areinvestigated from the viewpoint that the initial arities of all operations arearbitrary. Relations between operations arising from the structure definitions,however, lead to the restrictions which determine their possible arityshapes and lead us to formulate a partial arity freedom principle. Polyadicvector spaces and algebras, dual vector spaces, direct sums, tensor productsand inner pairing spaces are reconsidered.
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