Abstract

: We use classical results on the lattice L(B) of varieties of band (idempotent) semigroups to obtain information on the structure of the lattice P s(DA) of subpseudovarieties of DA, --- where DA is the largest pseudovariety of finite semigroups in which all regular semigroups are band semigroups. We bring forward a lattice congruence on P s(DA), whose quotient is isomorphic to L(B), and whose classes are intervals with effectively computable least and greatest members. Also we characterize the pro-identities satisfied by the members of an important family of subpseudovarieties of DA. Finally, letting V k be the pseudovariety generated by the k-generated elements of DA (k 1), we use all our results to compute the position of the congruence class of V k in L(B). Introduction The lattice of pseudovarieties of finite semigroups has been the object of much attention over the past few decades, with motivations drawn not only from universal algebra, but also from theoretical computer scie...

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