Conditions of modularity of the congruence lattice of an act over a rectangular band
Игорь Борисович Кожухов, A. M. Pryanichnikov, Aigul' Rimzilovna Simakova · Izvestiya Mathematics · 2019
Abstract We describe acts over rectangular bands that have modular, distributive or linearly ordered congruence lattice. It turns out that such acts have at most 11 elements, and their congruence lattice has at most 300 elements. Furthermore, certain facts are established about the structure of acts with modular congruence lattice over an arbitrary semigroup and about the structure of the congruence lattice of an act over a rectangular band. The work is based on the description of acts over a completely (0-)simple semigroup obtained by Avdeev and Kozhukhov in 2000 and on the characterization of disconnected acts with modular or distributive congruence lattice by Ptakhov and Stepanova in 2013.