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Original Articles

Structure of free strong doppelsemigroups

Pages 3262-3279 | Received 30 Apr 2017, Published online: 03 Jan 2018

References

  • Aguiar, M., Livernet, M. (2007). The associative operad and the weak order on the symmetric groups. J. Homotopy Relat. Struct. 2(1):57–84.
  • Boyd, S. J., Gould, M. (1999). Interassociativity and isomorphism. Pure Math. Appl. 10(1):23–30.
  • 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.
  • Clifford, A. H., Preston, G. B. (1961). The algebraic theory of semigroups. Vol. I. Am. Math. Soc., Providence, RI.
  • Drouzy, M. (1986). La structuration des ensembles de semigroupes d’ordre 2, 3 et 4 par la relation d’interassociativité. Manuscript.
  • Givens, B. N., Linton, K., Rosin, A., Dishman, L. (2007). Interassociates of the free commutative semigroup on n generators. Semigroup Forum 74:370–378.
  • Givens, B. N., Rosin, A., Linton, K. (2017). Interassociates of the bicyclic semigroup. Semigroup Forum 94:104–122. DOI: 10.1007/s00233-016-9794-9.
  • Gorbatkov, A. B. (2013). Interassociates of the free commutative semigroup. Sib. Math. J. 54(3):441–445.
  • Gorbatkov, A. B. (2014). Interassociates of a free semigroup on two generators. Mat. Stud. 41:139–145.
  • Gould, M., Linton, K. A., Nelson, A. W. (2004). Interassociates of monogenic semigroups. Semigroup Forum 68: 186–201.
  • Gould, M., Richardson, R. E. (1983). Translational hulls of polynomially related semigroups. Czechoslovak Math. J. 33(1):95–100.
  • 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.
  • Hickey, J. B. (1983). Semigroups under a sandwich operation. Proc. Edinburgh Math. Soc. 26:371–382.
  • Hickey, J. B. (1986). On variants of a semigroup. Bull. Austral. Math. Soc. 34(3):447–459.
  • Ljapin, E. (1960). Polugruppy. (Russian) [Semigroups] Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow.
  • Loday, J.-L. (2001). Dialgebras. In: Dialgebras and Related Operads, Lecture Notes Mathematics, Vol. 1763. Berlin: Springer-Verlag, pp. 7–66.
  • Loday, J.-L., Ronco, M. O. (2002). Order structure on the algebra of permutations and of planar binary trees. J. Algebraic Combin. 15:253–270.
  • Loday, J.-L., Ronco, M. O. (2004). Trialgebras and families of polytopes. Contemp. Math. 346:369–398.
  • Magill, Jr., K, ., Misra, P., Tewari, U. (1982). Structure spaces for sandwich semigroups. Pacific J. Math. 99(2):399–412.
  • Movsisyan, Yu. M. (1986). Introduction to the Theory of Algebras with Hyperidentities. Yerevan: Yerevan State University Press (in Russian).
  • Movsisyan, Yu. M. (1998). Hyperidentitties in algebras and varieties. Russ. Math. Surveys 53(1):57–108.
  • Pirashvili, T. (2003). Sets with two associative operations. Cent. Eur. J. Math. 2:169–183.
  • Richter, B. (1997). Dialgebren, Doppelalgebren und ihre Homologie. Diplomarbeit, Universitat Bonn. Available at: http://www.math.uni-hamburg.de/home/richter/publications.html.
  • Schein, B. M. (1965). Restrictive bisemigroups. Izv. Vyssh. Uchebn. Zaved. Mat. 1(44):168–179 (in Russian).
  • Zhuchok, A. V. (2009). Commutative dimonoids. Algebra Discrete Math. 2:116–127.
  • Zhuchok, A. V. (2010). Free commutative dimonoids. Algebra Discrete Math. 9(1):109–119.
  • Zhuchok, A. V. (2011). Dimonoids. Algebra Logic 50(4):323–340.
  • Zhuchok, A. V. (2011). Free dimonoids. Ukr. Math. J. 63(2):196–208.
  • Zhuchok, A. V. (2013). Free n-nilpotent dimonoids. Algebra Discrete Math. 16(2):299–310.
  • Zhuchok, A. V. (2013). Free products of dimonoids. Quasigroups Relat. Syst. 21(2):273–278.
  • Zhuchok, A. V. (2014). Elements of dimonoid theory. Mathematics and its Applications. In: Proceedings of Institute of Mathematics of NAS of Ukraine, Monograph, Kiev, , Vol. 98, 304 p. (in Ukrainian).
  • Zhuchok, A. V. (2015). Trioids. Asian-Eur. J. Math. 8(4):1550089 (23 p.). DOI: 10.1142/S1793557115500898.
  • Zhuchok, A. V. (2017). Free left n-dinilpotent doppelsemigroups. Commun. Algebra 45(11):4960–4970. DOI: 10.1080/00927872.2017. 1287274.
  • Zhuchok, A. V. (2017). Free products of doppelsemigroups. Algebra Univ. 77(3):361–374. DOI: 10.1007/ s00012-017-0431-6.
  • Zhuchok, A. V. (2017). Structure of relatively free dimonoids. Commun. Algebra 45(4):1639–1656. DOI: 10.1080/00927872.2016. 1222404.
  • Zhuchok, A. V., Demko, M. (2016). Free n-dinilpotent doppelsemigroups. Algebra Discrete Math. 22(2):304–316.
  • Zhuchok, A. V., Gorbatkov, A. B. (2017). On the structure of dimonoids. Semigroup Forum 94(2):194–203. DOI: 10.1007/s00233-016-9795-8.
  • 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.
  • Zupnik, D. (1971). On interassociativity and related questions. Aequationes Math. 6(2):141–148.

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