Special elements of certain types in the lattice of epigroup varieties

Lower-modular, codistributive and costandard elements of the lattice of all epigroup varieties are studied. Lower-modular and costandard elements are completely classified, and codistributive elements are described within a wide class of epigroup varieties that includes all commutative varieties. In particular, we verify that, in the lattice of all epigroup varieties, an element is costandard if and only if it is neutral and an element is modular whenever it is lower-modular.