On the semilattice of all finitely generated subsemigroups of a semigroup

Authors

DOI:

https://doi.org/10.17721/1812-5409.2024/2.2

Keywords:

semigroup, finitely generated semigroup, lattice of subsemigroups, semilattice of finitely generated subsemigroups

Abstract

This article is dedicated to the upper semilattice FSub(S) of all finitely generated subsemigroups of a semigroup S. We prove some necessary and sufficient conditions for this semilattice to form a lattice or to be a complete semilattice and describe some of its atoms and dual atoms. Studied were also finitely generated semigroups, all of whose finitely generated subsemigroups are finite, and lattices of their finitely generated subsemigroups. A sufficient condition for such a semigroup to be finite was found.

Pages of the article in the issue: 10 - 13

Language of the article: English

References

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Published

2025-01-29

How to Cite

Arskyi, N. (2025). On the semilattice of all finitely generated subsemigroups of a semigroup. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, 79(2), 10–13. https://doi.org/10.17721/1812-5409.2024/2.2

Issue

Section

Algebra, Geometry and Probability Theory