Endomorphisms of free abelian monogenic digroups

Yu. V. Zhuchok

doi:10.15330/ms.43.2.144-152

1. Loday J.-L., Dialgebras, in: Dialgebras and related operads, Lect. Notes Math., 1763 (2001) Springer- Verlag, Berlin, 7–66.

2. Liu K., Transformation digroups, preprint, available at http://arxiv.org/abs/math/0409265.

3. Kinyon M.K., Leibniz algebras, Lie racks, and digroups, J. Lie Theory, 17 (2007), №1, 99–114.

4. Phillips J.D., A short basis for the variety of digroups, Semigroup Forum, 70 (2005), 466–470.

5. Crompton C., Scalici L., The structure of digroups, American Journal of Undergraduate research, 5 (2006), №2, 21–27.

6. Felipe R., Generalized Loday algebras and digroups, Comunicaciones del CIMAT, №I-04-01/21-01-2004.

7. Liu K., The generalizations of groups, Research Monographs in Math., V.1, 153 Publishing: Burnaby, 2004.

8. Zhuchok A.V., Dimonoids, Algebra and Logic, 50 (2011), №4, 323–340.

9. Zhuchok A.V., Free commutative dimonoids, Algebra and Discrete Mathematics, 9 (2010), №1, 109–119.

10. Zhuchok Yu.V., Representations of ordered dimonoids by binary relations, Asian-European J. Math., 7 (2014), 1–13.

	Endomorphisms of free abelian monogenic digroups
Author	Yu. V. Zhuchok zhuchok_y@mail.ru Kyiv National Taras Schevchenko University, Faculty of Mechanics and Mathematics
Abstract	We construct a free abelian monogenic digroup and describe its endomorphism semigroup.
Keywords	free abelian digroup; dimonoid; congruence; endomorphism
DOI	doi:10.15330/ms.43.2.144-152
Reference	1. Loday J.-L., Dialgebras, in: Dialgebras and related operads, Lect. Notes Math., 1763 (2001) Springer- Verlag, Berlin, 7–66. 2. Liu K., Transformation digroups, preprint, available at http://arxiv.org/abs/math/0409265. 3. Kinyon M.K., Leibniz algebras, Lie racks, and digroups, J. Lie Theory, 17 (2007), №1, 99–114. 4. Phillips J.D., A short basis for the variety of digroups, Semigroup Forum, 70 (2005), 466–470. 5. Crompton C., Scalici L., The structure of digroups, American Journal of Undergraduate research, 5 (2006), №2, 21–27. 6. Felipe R., Generalized Loday algebras and digroups, Comunicaciones del CIMAT, №I-04-01/21-01-2004. 7. Liu K., The generalizations of groups, Research Monographs in Math., V.1, 153 Publishing: Burnaby, 2004. 8. Zhuchok A.V., Dimonoids, Algebra and Logic, 50 (2011), №4, 323–340. 9. Zhuchok A.V., Free commutative dimonoids, Algebra and Discrete Mathematics, 9 (2010), №1, 109–119. 10. Zhuchok Yu.V., Representations of ordered dimonoids by binary relations, Asian-European J. Math., 7 (2014), 1–13.
Pages	144-152
Volume	43
Issue	1
Year	2015
Journal	Matematychni Studii
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