We characterize the least semilattice congruence of a free dimonoid and prove that a free dimonoid is a semilattice of s-simple subdimonoids each of which is a rectangular band of subdimonoids.
KeywordsTriple System Bijective Mapping Leibniz Algebra Rectangular Band Free Semigroup
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- 2.J.-L. Loday, “Dialgebras,” in: J.-L. Loday, A. Frabetti, F. Chapoton, and F. Goichot (editors), Dialgebras and Related Operads, Springer (2001), pp. 7–66.Google Scholar
- 4.R. Felipe, Generalized Loday Algebras and Digroups, Comunicaciones del CIMAT, No. I-04-01/21-01-2004 (2004).Google Scholar
- 7.A. V. Zhuchok, “Commutative dimonoids,” Algebra Discr. Math., No. 2, 116–127 (2009).Google Scholar
- 10.A. V. Zhuchok, “The least semilattice congruence of a dimonoid,” Visn. Kyiv. Univ., Ser. Fiz.-Mat., Issue 3, 22–24 (2009).Google Scholar
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