Special elements in the lattice of overcommutative semigroup varieties revisited
V. Yu. Shaprynskii, B. M. Vernikov
TL;DR
This paper fully characterizes key elements in the lattice of overcommutative semigroup varieties, correcting previous inaccuracies and providing a comprehensive understanding of their distributive, codistributive, standard, costandard, and neutral properties.
Contribution
It offers a complete classification of specific lattice elements in overcommutative semigroup varieties, addressing and correcting prior gaps in the literature.
Findings
Identified all distributive elements in the lattice.
Determined all codistributive and standard elements.
Corrected previous inaccuracies in the classification.
Abstract
We completely determine all distributive, codistributive, standard, costandard, and neutral elements in the lattice of overcommutative semigroup varieties, thus correcting a gap contained in an earlier article by the second author.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Commutative Algebra and Its Applications