Special elements in lattices of semigroup varieties

The project is devoted to the systematic development of research on lattices of semigroup varieties. In recent years, extensive information on the special elements of the SEM lattice of all varieties of semigroups and the lattice EPI of all varieties of epigroups (semigroups, some degree of each element of which is a group element) has been obtained with the participation of the project executors. A number of types of special elements could be described completely, for others, conditions or descriptions in special cases were obtained. The project assumes continuation of the further consideration of this circle of questions. In particular, modular and cancellable elements of the SEM and EPI lattices will be considered. For the first of these types of elements, a number of results have been obtained to date, but the question of their full description remains open. The contractible elements of the SEM and EPI lattices were not previously considered in practice.