Popovich, Alexander L. Finite nilsemigroups with modular congruence lattices. (English) Zbl 1446.20077 Ural Math. J. 3, No. 1, 52-67 (2017). Summary: This paper continues the joint work [Semigroup Forum 95, No. 2, 314–320 (2017; Zbl 1422.20029)] of the author with P. R. 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. MSC: 20M10 General structure theory for semigroups 08A30 Subalgebras, congruence relations 06C05 Modular lattices, Desarguesian lattices Keywords:semigroup; nilsemigroup; congruence lattice Citations:Zbl 1422.20029 PDF BibTeX XML Cite \textit{A. L. Popovich}, Ural Math. J. 3, No. 1, 52--67 (2017; Zbl 1446.20077) Full Text: DOI MNR OpenURL References: [1] Nagy A., Jones P.R., “Permutative semigroups whose congruences form a chain”, Semigroup Forum, 69:3 (2004), 446-456 · Zbl 1074.20038 [2] Popovich A.L., Jones P.R., “On congruence lattices of nilsemigroups”, Semigroup Forum, 2016, 1-7 · Zbl 1422.20029 [3] Schein B.M., “Commutative semigroups where congruences form a chain”, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 17 (1969), 523-527 · Zbl 0187.29103 [4] Tamura T., “Commutative semigroups whose lattice of congruences is a chain”, Bull. Soc. Math. France, 97 (1969), 369-380 · Zbl 0191.01705 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.