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Complete semigroups of binary relations defined by finite XI-semilattices of unions

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Abstract

We give conditions under which the X-semilattice of unions is an XI-semilattice, i.e., let D be a finite X-semilattice of unions. The complete semigroup of binary relation B X (D) is defined by the XI-semilattice of unions if and only if V (D, β) = D for some β ∈ B X (D).

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References

  1. Ya. I. Diasamidze, “Complete semigroups of binary relations. Semigroups of binary relations,” J. Math. Sci., 117, No. 4, 4271–4319 (2003).

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  2. Ya. Diasamidze and Sh. Makharadze, “Complete semigroups of binary relations defined by X-semilattices of unions,” J. Math. Sci., 166, No. 5, 615–633 (2010).

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Authors and Affiliations

  1. Shota Rustaveli Batumi State University, Batumi, Georgia

    Ya. Diasamidze & Sh. Makharadze

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  1. Ya. Diasamidze
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  2. Sh. Makharadze
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Correspondence to Ya. Diasamidze.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 74, Proceedings of the International Conference “Modern Algebra and Its Applications” (Batumi, 2010), Part 1, 2011.

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Diasamidze, Y., Makharadze, S. Complete semigroups of binary relations defined by finite XI-semilattices of unions. J Math Sci 186, 723–725 (2012). https://doi.org/10.1007/s10958-012-1023-9

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  • DOI: https://doi.org/10.1007/s10958-012-1023-9

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