Geodesic
Free abelian dimonoids
Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 330-342.

Voir la notice de l'article provenant de la source Math-Net.Ru

We construct a free abelian dimonoid and describe the least abelian congruence on a free dimonoid. Also we show that free abelian dimonoids are determined by their endomorphism semigroups.
Keywords: free abelian dimonoid, abelian dimonoid, congruence, endomorphism semigroup. 
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Yurii V. Zhuchok. Free abelian dimonoids. Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 330-342. http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a10/

[1] Loday J.-L., “Dialgebras”, Dialgebras and related operads, Lect. Notes Math., 1763, Springer-Verlag, Berlin, 2001, 7–66 | DOI | MR | Zbl

[2] Kinyon M. K., “Leibniz algebras, Lie racks, and digroups”, J. Lie Theory, 17:1 (2007), 99–114 | MR | Zbl

[3] Liu K., “The Generalizations of groups”, Research Monographs in Math., 1 (2004), 153 Publishing, Burnaby

[4] Pirashvili T., “Sets with two associative operations”, Cent. Eur. J. Math., 2 (2003), 169–183 | DOI | MR | Zbl

[5] Zhuchok Yu. V., “Representations of ordered dimonoids by binary relations”, Asian-European J. Math., 07 (2014), 1450006-1–1450006-13 | DOI | MR

[6] Zhuchok A. V., “Free dimonoids”, Ukr. Math. J., 63:2 (2011), 196–208 | DOI | MR | Zbl

[7] Zhuchok A. V., “Free commutative dimonoids”, Algebra and Discrete Mathematics, 9:1 (2010), 109–119 | MR

[8] Zhuchok A. V., “Free normal dibands”, Algebra and Discrete Math., 12:2 (2011), 112–127 | MR | Zbl

[9] Zhuchok A. V., “Free $(lr,rr)$-dibands”, Algebra Discrete Math., 15:2 (2013), 295–304 | MR | Zbl

[10] Birkhoff G., “On the structure of abstract algebras”, Proc. Cambr. Phil. Soc., 31 (1935), 433–454 | DOI

[11] Felipe R., “Generalized Loday algebras and digroups”, Comunicaciones del CIMAT, I-04-01/21-01-2004

[12] Ulam S. M., A Collection of Mathematical Problems, Interscience Publishers, New York, 1960 | MR | Zbl

[13] Plotkin B. I., Seven Lectures on the Universal Algebraic Geometry, Preprint, Institute of Mathematics, Hebrew University, 2000

[14] Formanek E., “A question of B. Plotkin about the semigroup of endomorphisms of a free group”, Proc. American Math. Society, 130 (2001), 935–937 | DOI | MR

[15] Mashevitsky G., Schein B. M., “Automorphism of the endomorphism semigroup of a free monoid or a free semigroup”, Proceedings of the AMS, 131:6 (2003), 1655–1660 | DOI | MR

[16] Zhuchok Yu. V., “The endomorphism semigroup of a free dimonoid of rank 1”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 76:3 (2014), 30–37 | MR

[17] Zhuchok Yu. V., “On determinability of free trioids by endomorphism semigroups”, Dopovidi NANU, 2015, no. 4, 7–11 (Russian) | MR | Zbl