An additive group on which some (scalar) field has an associative multIPlicative action which distributes over the addition of the vector space and respects the addition of the (scalar) field: for vectors u, v and scalars h, k h(u+v) = hu + hv (h+k)u = hu + ku (hk)u = h(ku). [Simple example?] (1996-09-30)
