Some simple algebraic properties, described by universally quantified disjunctions of special identities, are established. Such sentences seem to be useful for an investigation on finite algebras and its products. These considerations are exemplified by results concerning distributive lattices. By P the polynomial algebra of a finite type t is understood. P is the n-ary polynomial algebra . No notational distinction is made between an algebra and its underlying set. Similarly by the same symbol is denoted each polynomial and its realization (...) in a given algebra. (shrink)