Monadic MV-algebras I: a study of subvarieties

In this paper, we study and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra 0, 1] ^k . We describe completely the lattice of subvarieties of the subvariety ${\mathcal{V}({\bf 0}, {\bf 1}]^k)}$ generated by 0, 1] ^k . We prove that the subvariety generated by a subdirectly irreducible monadic MV-algebra of finite width depends on the order and rank of ?A, the partition associated to A of the set of coatoms of the boolean subalgebra B(A) of its complemented elements, and the width of the algebra. We also give an equational basis for each proper subvariety in ${\mathcal{V}({\bf 0}, {\bf 1}]^k)}$ . Finally, we give some results about subvarieties of infinite width.