FINITE NILSEMIGROUPS WITH MODULAR CONGRUENCE LATTICES

Alexander L. Popovich     (Ural Federal University, Ekaterinburg, Russian Federation)

Abstract


This paper continues the joint work [2] of the author with P. Jones. We describe all finitely generated nilsemigroups with modular congruence lattices: there are 91 countable series of such semigroups. For finitely generated nilsemigroups a simple algorithmic test to the congruence modularity is obtained.


Keywords


semigroup, nilsemigroup, congruence lattice

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References


  1. Nagy A., Jones P.R. Permutative semigroups whose congruences form a chain // Semigroup Forum, 2004. Vol. 69, no. 3. P. 446–456. DOI: 10.1007/s00233-004-0131-3
  2. Popovich A.L., Jones P.R. On congruence lattices of nilsemigroups // Semigroup Forum, 2016. P. 1–7. DOI: 10.1007/s00233-016-9837-2
  3. Schein B.M. Commutative semigroups where congruences form a chain // Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 1969. Vol. 17. P. 523–527.
  4. Tamura T. Commutative semigroups whose lattice of congruences is a chain // Bull. Soc. Math. France, 1969. Vol. 97. P. 369–380.



DOI: http://dx.doi.org/10.15826/umj.2017.1.004

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