Structure of relatively free dimonoids

References

• Bokut, L. A., Chen, Y.-Q., Liu, C.-H. (2010). Gröbner–Shirshov bases for dialgebras. Int. J. Algebra Comput. 20(3):391–415.
   Web of Science ®Google Scholar
• Boyd, S. J., Gould, M., Nelson, A. W. (1997). Interassociativity of semigroups. In: Proceedings of the Tennessee Topology Conference, Nashville, TN, USA, 1996. Singapore: World Scientific, pp. 33–51.
   Google Scholar
• Drouzy, M. (1986). La structuration des ensembles de semigroupes d’ordre 2, 3 et 4 par la relation d’interassociativité. Manuscript.
   Google Scholar
• Frabetti, A. (2001). Dialgebra (co)homology with coefficients. In: Dialgebras and Related Operads: Lect. Notes Math., Vol. 1763. Berlin: Springer-Verlag, pp. 67–103.
   Google Scholar
• Givens, B. N., Linton, K., Rosin, A., Dishman, L. (2007). Interassociates of the free commutative semigroup on n generators. Semigroup Forum 74:370–378.
   Web of Science ®Google Scholar
• Gould, M., Linton, K. A., Nelson, A. W. (2004). Interassociates of monogenic semigroups. Semigroup Forum 68:186–201.
   Web of Science ®Google Scholar
• Gould, M., Richardson, R. E. (1983). Translational hulls of polynomially related semigroups. Czechoslovak Math. J. 33(1):95–100.
   Web of Science ®Google Scholar
• Hewitt, E., Zuckerman, H. S. (1969). Ternary operations and semigroups. In: Folley, K.W., ed, Semigroups: Proceedings 1968 Wayne State U. Symposium on Semigroups, New York: Academic Press, pp. 55–83.
   Google Scholar
• Kinyon, M. K. (2007). Leibniz algebras, Lie racks, and digroups. J. Lie Theory 17(4):99–114.
   Google Scholar
• Kolesnikov, P. S. (2008). Varieties of dialgebras and conformal algebras. Sib. Math. J. 49(2):257–272.
   Web of Science ®Google Scholar
• Kolesnikov, P. S., Voronin, V. Yu. (2013). On the special identities for dialgebras. Linear and Multilinear Algebra 61(3):377–391.
   Web of Science ®Google Scholar
• Koreshkov, N. A. (2008). n-Tuple algebras of associative type. Izv. Vyssh. Uchebn. Zaved. Mat. 12:34–42. (in Russian).
   Google Scholar
• Liu, K. A. (2004). A class of ring-like objects. Preprint, Available at: http://arxiv.org/abs/math/0411586v2.
   Google Scholar
• Loday, J.-L. (1993). Une version non commutative des algèbres de Lie: les algèbres de Leibniz. Ens. Math. 39:269–293.
   Google Scholar
• Loday, J.-L. (2001). Dialgebras. In: Dialgebras and Related Operads: Lect. Notes Math., Vol. 1763, Berlin: Springer-Verlag, pp. 7–66.
   Google Scholar
• Loday, J.-L., Ronco, M. O. (2004). Trialgebras and families of polytopes. Contemp. Math. 346:369–398.
   Google Scholar
• Petrich, M., Silva, P. V. (2002). Structure of relatively free bands. Commun. Algebra 30(9):4165–4187.
   Web of Science ®Google Scholar
• Phillips, J. D. (2005). A short basis for the variety of digroups. Semigroup Forum 70:466–470.
   Web of Science ®Google Scholar
• Pirashvili, T. (2003). Sets with two associative operations. Cent. Eur. J. Math. 2:169–183.
   Google Scholar
• Pozhidaev, A. P. (2009). 0-Dialgebras with bar-unity and nonassociative Rota–Baxter algebras. Sib. Math. J. 50(6):1070–1080.
   Web of Science ®Google Scholar
• Richter, B. (1997). Dialgebren, Doppelalgebren und ihre Homologie. Diplomarbeit, Universitat Bonn, Available at: http://www.math.uni-hamburg.de/home/richter/publications.html.
   Google Scholar
• Schein, B. M. (1964). One-sided nilpotent semigroups. Uspekhi Mat. Nauk 19 1(115):187–189. (in Russian).
   Google Scholar
• Schein, B. M. (1965). Restrictive bisemigroups. Izv. Vyssh. Uchebn. Zaved. Mat. 1(44):168–179. (in Russian).
   Google Scholar
• Schein, B. M. (1989). Restrictive Semigroups and Bisemigroups. Technical Report. Fayetteville, Arkansas, USA: University of Arkansas, 1–23.
   Google Scholar
• Zhuchok, A. V. (2009). Commutative dimonoids. Algebra Discrete Math. 3:116–127.
   Google Scholar
• Zhuchok, A. V. (2010). Free commutative dimonoids. Free commutative dimonoids. 9(1):109–119.
   Google Scholar
• Zhuchok, A. V. (2011). Free dimonoids. Ukr. Math. J. 63(2):196–208.
   Web of Science ®Google Scholar
• Zhuchok, A. V. (2011). Free normal dibands. Algebra Discrete Math. 12(2):112–127.
   Google Scholar
• Zhuchok, A. V. (2011). Free rectangular dibands and free dimonoids. Algebra Discrete Math. 11(2):92–111.
   Google Scholar
• Zhuchok, A. V. (2011). Dimonoids. Algebra Logic 50(4):323–340.
   Web of Science ®Google Scholar
• Zhuchok, A. V. (2011). Dimonoids with an idempotent operation. Proc. Inst. Appl. Math. Mech. 22:99–107. (in Ukrainian).
   Google Scholar
• Zhuchok, A. V. (2011). Some least congruences on dimonoids. Visnyk Kyiv. Univ. Ser. Phis.-Math. Nauku 4:7–10.
   Google Scholar
• Zhuchok, A. V. (2012). Decompositions of free dimonoids. Decompositions of free dimonoids. 154(2):93–100. (in Russian).
   Google Scholar
• Zhuchok, A. V. (2013). Free (ℓr,rr)-dibands. Free (ℓr,rr)-dibands. 15(2):295–304.
   Google Scholar
• Zhuchok, A. V. (2013). Free n-dinilpotent dimonoids. Prob. Phys. Math. Tech. 17(4):43–46.
   Google Scholar
• Zhuchok, A. V. (2013). Free n-nilpotent dimonoids. Algebra Discrete Math. 16(2):299–310.
   Google Scholar
• Zhuchok, A. V. (2013). Free products of dimonoids. Quasigroups Relat. Syst. 21(2):273–278.
   Google Scholar
• Zhuchok, A. V. (2014). Elements of dimonoid theory. Mathematics and its Applications. In: Proceedings of Institute of Mathematics of NAS of Ukraine, Monograph, Kiev. (in Ukrainian).
   Google Scholar
• Zhuchok, A. V. (2015). Dimonoids and bar-units. Sib. Math. J. 56(5):827–840.
   Web of Science ®Google Scholar
• Zhuchok, A. V., Zhuchok, Yul. V. (2016). Free left n-dinilpotent dimonoids. Semigroup Forum 93(1):161–179. doi: 10.1007/s00233-015-9743-z.
   Web of Science ®Google Scholar
• Zhuchok, A. V., Zhuchok, Yu. V. (2016). On two classes of digroups. São Paulo J. Math. Sci. doi: 10.1007/s40863-016-0038-4.
   Google Scholar
• Zhuchok, Y. V. (2015). Free abelian dimonoids. Algebra Discrete Math. 20(2):330–342.
   Web of Science ®Google Scholar