12 citations · 27 across the 5 of their papers we have counts for
9 papers
Proving at Scale for Universal Algebra
João Araújo, Jan Hůla, Mikoláš Janota +2
We introduce SemiBase, a project that computes and formally certifies finite identity bases for small semigroups. Deciding finite basability is undecidable for finite algebras and…
Characterization of Cross varieties of -trivial monoids
Sergey V. Gusev, Edmond W. H. Lee, Wen Ting Zhang
A finitely based, finitely generated variety with finitely many subvarieties is a Cross variety. In the present article, it is shown that a variety of -trivial monoids is Cross…
Finite basis problem for involution semigroups of order four
Meng Gao, Wen Ting Zhang, Yan Feng Luo
Recently, we have found a non-finitely based involution semigroup of order five. It is natural to question what is the smallest order of non-finitely based involution semigroups. I…
Cancellable elements of the lattice of monoid varieties
Sergey V. Gusev, Edmond W. H. Lee
The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the l…
The lattice of varieties of monoids
Sergey V. Gusev, Edmond W. H. Lee, Boris M. Vernikov
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems…
Varieties of monoids with complex lattices of subvarieties
Sergey V. Gusev, Edmond W. H. Lee
A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been…
A Survey on Varieties Generated by Small Semigroups and a Companion Website
João Araújo, João Pedro Araújo, Peter J. Cameron +2
The aim of this paper is to provide an atlas of identity bases for varieties generated by small semigroups and groups. To help the working mathematician easily find information, we…
Join irreducible semigroups
Edmond W. H. Lee, John Rhodes, Benjamin Steinberg
We begin a systematic study of finite semigroups that generate join irreducible members of the lattice of pseudovarieties of finite semigroups, which are important for the spectral…
Monoid varieties with extreme properties
Marcel Jackson, Edmond W. H. Lee
Finite monoids that generate monoid varieties with uncountably many subvarieties seem rare, and surprisingly, no finite monoid is known to generate a monoid variety with countably…