Cancellable elements of the lattice of semigroup varieties: varieties satisfying a permutational identity of length 3
Boris M. Vernikov
TL;DR
This paper classifies semigroup varieties satisfying a specific permutational identity of length 3 that are cancellable in the lattice of all semigroup varieties, and provides examples of modular but not cancellable varieties.
Contribution
It completely characterizes cancellable elements satisfying a permutational identity of length 3 in the lattice of semigroup varieties.
Findings
Identified all semigroup varieties satisfying the permutational identity of length 3 that are cancellable.
Provided new examples of modular but non-cancellable semigroup varieties.
Abstract
We completely determine all semigroup varieties satisfiyng a permutational identity of length 3 that are cancellable elements of the lattice of all semigroup varieties. Using this result, we provide a series of new examples of semigroup varieties that are a modular but not cancellable elements of this lattice.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Commutative Algebra and Its Applications