Special elements in lattices of semigroup varieties

2013/09/01 by B. M. Vernikov, Vernikov, B. M. · 2 citations
Computer Science · #08B15 (Secondary) #20M07 (Primary) #Advanced Algebra and Logic #FOS: Mathematics #Group Theory (math.GR) #Rough Sets and Fuzzy Logic #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1309.0228

openalex publication_date 2013/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey results concerning special elements of nine types (modular, lower-modular, upper-modular, cancellable, distributive, codistributive, standard, costandard and neutral elements) in the lattice of all semigroup varieties and certain its sublattices, mainly in the lattices of all commutative varieties and of all overcommutative ones. Several open questions are formulated. The work is regularly updated and modified as new results and/or articles appear.

Cited by

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

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