Zhuchok, Anatolii V. Semilattices of subdimonoids. (English) Zbl 1232.08002 Asian-Eur. J. Math. 4, No. 2, 359-371 (2011). Summary: We present some congruence on the dimonoid with an idempotent operation and use it to obtain semilattice decompositions of an idempotent dimonoid. Also we give necessary and sufficient conditions under which an arbitrary dimonoid is a semilattice of archimedean subdimonoids. Cited in 11 Documents MSC: 08A05 Structure theory of algebraic structures 08A30 Subalgebras, congruence relations 20M99 Semigroups Keywords:dimonoid; idempotent operation; idempotent dimonoid; semilattice of subdimonoids; semigroup PDFBibTeX XMLCite \textit{A. V. Zhuchok}, Asian-Eur. J. Math. 4, No. 2, 359--371 (2011; Zbl 1232.08002) Full Text: DOI References: [1] DOI: 10.1007/3-540-45328-8_2 · doi:10.1007/3-540-45328-8_2 [2] Zhuchok A. V., Algebra and Discr. Math. 2 pp 116– [3] Zhuchok A. V., Algebra and Discr. Math. 9 pp 109– [4] Pirashvili T., Central European J. Math. 2 pp 169– [5] DOI: 10.1007/s00233-004-0169-2 · Zbl 1095.20052 · doi:10.1007/s00233-004-0169-2 [6] Schein B. M., Izv. Vyssh. Uchebn. Zaved. Mat. 1 pp 168– [7] DOI: 10.1142/S0218196710005753 · Zbl 1245.17001 · doi:10.1142/S0218196710005753 [8] Kolesnikov P. S., Sib. Math. J. 49 pp 322– [9] Pozhidaev A. P., Sib. Math. J. 49 pp 870– [10] Kac V. G., University Lecture Series 10 (1996) [11] DOI: 10.2307/2307797 · Zbl 0055.01404 · doi:10.2307/2307797 [12] Clifford A. H., Proc. Amer. Math. Soc. 5 pp 449– [13] DOI: 10.1007/BF02389126 · Zbl 0262.20070 · doi:10.1007/BF02389126 [14] Clifford A.H., Amer. Math. Soc. 1 [15] DOI: 10.1016/0021-8693(69)90013-1 · Zbl 0187.29102 · doi:10.1016/0021-8693(69)90013-1 [16] Tamura T., Kodai Math. Sem. Rep. pp 109– [17] DOI: 10.3792/pja/1195519758 · Zbl 0251.20063 · doi:10.3792/pja/1195519758 [18] DOI: 10.1007/BF02572490 · Zbl 0524.20037 · doi:10.1007/BF02572490 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.