Varieties of algebras arising from K-perfect m-cycle systems Original Research Article

A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from image-perfect m-cycle systems form a variety for image only, and that the algebras arising from image-perfect m-cycle systems form a variety for image only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety.