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Irreducible Generating Sets of Complete Semigroups of Unions BX(D) Defined by Semilattices of the Class Σ1(X, 4)

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Abstract

In complete semigroups of unions BX(D) defined by semilattices of the class Σ1(X, 4), we describe the set of all external elements and show that it is a generating (and, therefore, irreducible) set of the semigroup BX(D). For a finite semigroup BX(D), we given a formula for calculating the number of elements of the generating set.

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References

  1. O. Givradze, “Irreducible generating sets of complete semigroups of unions BX(D) defined by semilattices of the class Σ2(X, 4),” J. Math. Sci., 186, No. 5, 745–750 (2012).

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  2. O. Givradze, “The number of equivalences on a finite set,” Proc. A. Razmadze Math. Inst., 131, 121–122 (2003).

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  1. Shota Rustaveli Batumi State University, Batumi, Georgia

    O. Givradze

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  1. O. Givradze
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Correspondence to O. Givradze.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 177, Algebra, 2020.

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Givradze, O. Irreducible Generating Sets of Complete Semigroups of Unions BX(D) Defined by Semilattices of the Class Σ1(X, 4). J Math Sci 275, 718–721 (2023). https://doi.org/10.1007/s10958-023-06712-7

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