초록 close

Clones are sets of operations which are closed under composition and contain all projections. Identities of clones of term operations of a given algebra correspond to hyperidentities of this algebra, i.e., to identities which are satisfied after any replacements of fundamental operations by derived operations ([7]). If any identity of an algebra is satisfied as a hyperidentity, the algebra is called solid ([3]). Solid algebras correspond to free clones. These connections will be extended to so-called generalized clones, to strong hyperidentities and to strongly solid varieties. On the basis of a generalized superposition operation for terms we generalize the concept of a unitary Menger algebra of finite rank([6]) to unitary Menger algebras with infinitely many nullary operations and prove that strong hyperidentities correspond to identities in free unitary Menger algebras with infinitely many nullary operations.