Special elements in lattices of semigroup varieties

Abstract

We survey results concerning special elements of eight types (modular, lower-modular, upper-modular, distributive, codistributive, standard, costandard and neutral elements) in the lattice of all semigroup varieties and three of its sublattices, namely, the lattices of commutative varieties, of permutative varieties and of overcommutative ones. These results are due to Ježek, McKenzie, ShaprynskѤ, Volkov and the author. Several open questions are formulated. © Bolyai Institute, University of Szeged.