Geodesic
Free abelian trioids
Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 147-160.

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

We construct a free abelian trioid and describe the least abelian congruence on a free trioid.
Keywords: abelian trioid, free abelian trioid, congruence. 
@article{ADM_2021_32_1_a9,
     author = {Yu. V. Zhuchok},
     title = {Free abelian trioids},
     journal = {Algebra and discrete mathematics},
     pages = {147--160},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a9/}
}
TY  - JOUR
AU  - Yu. V. Zhuchok
TI  - Free abelian trioids
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 147
EP  - 160
VL  - 32
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a9/
LA  - en
ID  - ADM_2021_32_1_a9
ER  - 
%0 Journal Article
%A Yu. V. Zhuchok
%T Free abelian trioids
%J Algebra and discrete mathematics
%D 2021
%P 147-160
%V 32
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a9/
%G en
%F ADM_2021_32_1_a9
Yu. V. Zhuchok. Free abelian trioids. Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 147-160. http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a9/

[1] Clifford A. H., Preston G. B., The algebraic theory of semigroups, v. 1, Amer. Math. Soc., 1961, 224 pp. | MR | Zbl

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

[3] Huang J., Chen Yu., “Gröbner-Shirshov Bases Theory for Trialgebras”, Mathematics, 9 (2021), 1207 | DOI

[4] Kurdachenko L. A., Semko N. N., Subbotin I. Ya., “The Leibniz algebras whose subalgebras are ideals”, Open Math., 15 (2017), 92–100 | DOI | MR | Zbl

[5] Loday J.-L., Ronco M. O., “Trialgebras and families of polytopes”, Contemp. Math., 346 (2004), 369–398 | DOI | MR | Zbl

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

[7] Movsisyan Y., Davidov S., Safaryan Mh., “Construction of free $g$-dimonoids”, Algebra Discrete Math., 18:1 (2014), 138–148 | MR | Zbl

[8] Naurazbekova A., “On the structure of free dual Leibniz algebras”, Eurasian Math. J., 10:3 (2019), 40–47 | DOI | MR | Zbl

[9] Rodríguez-Nieto J. G., Salazar-Díaz O. P., Velásquez R., “Abelian and symmetric generalized digroups”, Semigroup Forum, 102 (2021), 861–884 | DOI | MR | Zbl

[10] Sanchez-Ortega J., “On the definitions of nucleus for dialgebras”, J. Algebra, 392 (2013), 244–264 | DOI | MR | Zbl

[11] Vallette B., “Manin products, Koszul duality, Loday algebras and Deligne conjecture”, J. Reine Angew. Math., 620 (2008), 105–164 | MR | Zbl

[12] Zhang G., Chen Y., “A construction of the free digroup”, Semigroup Forum, 102 (2021), 553–567 | DOI | MR | Zbl

[13] Zhuchok A. V., Knauer K., “Abelian doppelsemigroups”, Algebra Discrete Math., 26:2 (2018), 290–304 | MR | Zbl

[14] Zhuchok A. V., Zhuchok Yul. V., Zhuchok Yu. V., “Certain congruences on free trioids”, Commun. Algebra, 47:12 (2019), 5471–5481 | DOI | MR | Zbl

[15] Zhuchok A. V., “Free commutative trioids”, Semigroup Forum, 98:2 (2019), 355–368 | DOI | MR | Zbl

[16] Zhuchok A. V., “Free products of dimonoids”, Quasigroups Rel. Syst., 21 (2013), 273–278 | MR | Zbl

[17] Zhuchok A. V., Zhuchok Yu.V., “On two classes of digroups”, São Paulo J. Math. Sciences, 11:1 (2017), 240–252 | DOI | MR | Zbl

[18] Zhuchok A. V., “Structure of relatively free trioids”, Algebra Discrete Math., 31:1 (2021), 152–166 | DOI | MR | Zbl

[19] Zhuchok A. V., “Trioids”, Asian-Eur. J. Math., 8:4 (2015), 1550089, 23 pp. | DOI | MR | Zbl

[20] Zhuchok Yul.V., “Decompositions of free trioids”, Bulletin of Taras Shevchenko National University of Kyiv. Series: Phys. Math., 2014, no. 4, 28–34 | Zbl

[21] Zhuchok Yu.V., “Automorphisms of the endomorphism semigroup of a free abelian diband”, Algebra Discrete Math., 25:2 (2018), 322–332 | MR | Zbl

[22] Zhuchok Yu.V., “Automorphisms of the endomorphism semigroup of a free commutative dimonoid”, Commun. Algebra, 45:9 (2017), 3861–3871 | DOI | MR | Zbl

[23] Zhuchok Yu.V., “Automorphisms of the endomorphism semigroup of a free commutative $g$-dimonoid”, Algebra Discrete Math., 21:2 (2016), 309–324 | MR | Zbl

[24] Zhuchok Yu.V., “Endomorphisms of free abelian monogenic digroups”, Mat. Studii, 43:2 (2015), 144–152 | DOI | MR | Zbl

[25] Zhuchok Yu.V., “Free abelian dibands”, Visnyk of the Lviv Univ. Series Mech. Math., 84 (2017), 15–21 | MR

[26] Zhuchok Yu.V., “Free abelian dimonoids”, Algebra Discrete Math., 20:2 (2015), 330–342 | MR | Zbl

[27] Zhuchok Yu.V., “On free abelian trioids”, Book of Abstracts of the 13th Intern. Algeb. Conf. in Ukraine (Kyiv, 6–9 July 2021), 89 | MR

[28] Zhuchok Yu.V., “On the determinability of free trioids by semigroups of endomorphisms”, Reports of the NAS of Ukraine, 4 (2015), 7–11 (in Russian) | MR | Zbl

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

[30] Zhuchok Yu.V., “The endomorphism monoid of a free trioid of rank 1”, Algebra Univers., 76:3 (2016), 355–366 | DOI | MR | Zbl

[31] 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 | Zbl