On modular and cancellable elements of the lattice of semigroup\n varieties

2017/09/09 by Dmitry V. Skokov, Skokov, Dmitry V., B. M. Vernikov +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Primary 20M07 #secondary 08B15 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1709.02944

openalex publication_date 2017/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We completely determine all semigroup varieties satysfiyng a permutational\nidentity of length 3 that are modular elements of the lattice of all semigroup\nvarieties. Using this result, we provide an example of a semigroup variety that\nis a modular but not cancellable element of this lattice.\n

Cited by

• Modular elements of the lattices of varieties of semigroups and epigroups. I

Related

• Cancellable elements of the lattice of semigroup varieties: varieties\n satisfying a permutational identity of length 3
• Cancellable elements of the lattices of varieties of semigroups and epigroups
• Lower-modular elements of the lattice of semigroup varieties. III
• Cancellable elements in the lattice of overcommutative semigroup varieties
• Special elements in lattices of semigroup varieties