Operators on the lattice of pseudovarieties of finite semigroups
On the lattice \(\mathbf{L(F)}\) of all pseudovarieties of finite semigroups the Mal'cev type operator \({\mathbf U}\mapsto{\mathbf U}M^+=L{\mathbf G}\circ{\mathbf U}\) (\(L{\mathbf G}\) denoting the pseudovariety of all local groups) and operators \(T_l^+\), \(T_r^+\), \(T^+\), \(K^+\), \(K_l^+\), \(K_r^+\), \(K_\iota^+\) are studied (each of which is defined in the above way, \(L{\mathbf G}\) being replaced with a certain sub-pseudovariety). Each of these operators comes from a radical congruence system on \(\mathbf F\). Various aspects of these operators are investigated. For example, pseudoidentity bases of \({\mathbf U}M^+\), \({\mathbf U}T_l^+\), etc., are presented in terms of pseudoidentity bases of \({\mathbf U}\). Moreover, each of these operators is shown to commute with the local operator \(L\) and the core operator \(C\).
scientific article; zbMATH DE number 1209921