The variety generated by the class of K-perfect m-cycle systems

A method called the standard construction generates an algebra from a K-perfect m-cycle system. Let C denote the class of algebras generated by K-perfect m-cycle systems. For each m and K, there is a known set Ε of identities which all the algebras in C satisfy. The question of when C is a variety is answered in [2]. When C is a variety it is defined by In general, C£ is a proper subclass of V(E*), the variety of algebras defined by Ε If the standard construction is applied to partial K-perfect mcycle systems then partial algebras result. Using these partial algebras we are able to investigate properties of V(Ε ). We show that the free algebras of V(Ε ) correspond to K-perfect m-cycle systems, so C generates V(Ε ). We also answer two questions asked in [5] concerning subvarieties of V(Ε ). Many of these results can be unified in the result that for any subset K' of K, V(Ε ) is generated by the class of algebras corresponding to finite K-perfect m-cycle systems