Abstract
It is known that if we know all XI-subsemilattices of a given X-semilattice of unions, then we can determine all idempotent elements of the semigroup, and the structure of idempotent elements is characterized. In this work, we find idempotent elements of the semigroup corresponding to X-semilattices of unions of the class Σ16(X, 6). Moreover, we give formulas for the number of idempotent elements, where X is finite.
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References
Ya. Diasamidze, Sh. Makharadze, and N. Rokva, “On XI-semilattices of unions,” Bull. Georgian Natl. Acad. Sci., 2, No. 1, 16–24 (2008).
Ya. Diasamidze, Sh. Makharadze, and I. Ya. Diasamidze, “Idempotents and regular elements of complete semigroups of binary relations,” J. Math. Sci., 153, No. 4 (2008).
Ya. Diasamidze and Sh. Makharadze, “Complete semigroups of binary relations” (not published).
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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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Erdoğan, A., Tekin, H.M. Idempotent elements of the semigroup corresponding to an X-semilattice of unions of the class Σ16(X, 6). J Math Sci 186, 741–744 (2012). https://doi.org/10.1007/s10958-012-1025-7
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DOI: https://doi.org/10.1007/s10958-012-1025-7