On Congruence Lattices of Nilsemigroups

Authors

Alexander L. Popovich, Ural Federal University
Peter Jones, Marquette UniversityFollow

Document Type

Article

Language

eng

Publication Date

10-2017

Publisher

Springer

Source Publication

Semigroup Forum

Source ISSN

0037-1912

Abstract

We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the semigroup, as a poset, is at most two, and distributive if and only if its width is one. In the latter case, such semigroups therefore coincide with the nil Δ">Δ Δ -semigroups. It is further shown that if a finitely generated nilsemigroup has modular congruence lattice, then the semigroup is finite.

Comments

Accepted version. Semigroup Forum, Vol. 95, No. 2 (October 2017): 314-320. DOI. © 2017 Springer International Publishing AG. Part of Springer Nature. Used with permission.

Shareable Link. Provided by the Springer Nature SharedIt content-sharing initiative.

Recommended Citation

Popovich, Alexander L. and Jones, Peter, "On Congruence Lattices of Nilsemigroups" (2017). Mathematics, Statistics and Computer Science Faculty Research and Publications. 525.
https://epublications.marquette.edu/mscs_fac/525