Finitely generated varieties of commutative BCK-algebras: covers

Abstract The article aims to describe all covers of every finitely generated variety of cBCK-algebras. It is known that subdirectly irreducible cBCK-algebras are rooted trees (with respect to their order). Moreover, all subdirectly irreducible members of a finitely generated variety are isomorphic to subalgebras of the subdirectly irreducible generators of that variety. The first part of the article focuses on subalgebras of finite subdirectly irreducible cBCK-algebras. The second and main part presents a construction that provides all the covers of any finitely generated variety, which constitutes the central contribution of the article.