227
Views
37
CrossRef citations to date
0
Altmetric
Original Articles

Binary Relations on Ternary Semihypergroups

&
Pages 3621-3636 | Received 09 Apr 2009, Published online: 24 Nov 2010

REFERENCES

  • Chronowski , A. ( 1996 ). On ternary semigroups of lattice homomorphisms . Quasigroups Related Systems 3 : 55 – 72 .
  • Chronowski , A. ( 2004 ). Congruences on ternary semigroups . Ukrainian Math. J. 56 : 662 – 681 .
  • Corsini , P. ( 1993 ). Prolegomena of Hypergroup Theory. , 2nd ed. Tricesimo , Italy : Aviani Editore .
  • Corsini , P. , Leoreanu , V. ( 2003 ). Applications of Hyperstructure Theory . Advances in Mathematics , Dordrecht : Kluwer Academic Publishers .
  • Davvaz , B. ( 2008 ). Approximations in n-ary algebraic systems . Soft Computing 12 : 409 – 418 .
  • Davvaz , B. , Dudek W. A., Vougiouklis , T. ( 2009 ). A generalization of n-ary algebraic systems . Communications in Algebra 37 : 1248 – 1263 .
  • Davvaz , B. , Dudek , W. A. , Mirvakili , S. ( 2009 ). Neural elements, fundamental relations and n-ary hypersemigroups . International Journal of Algebra and Computation 19 : 567 – 583 .
  • Davvaz , B. , Leoreanu-Fotea , V. ( 2007 ). Hyperring Theory and Applications . Palm Harbor , USA : International Academic Press, Inc .
  • Davvaz , B. , Vougiouklis , T. ( 2006 ). n-ary hypergroups . Iranian Journal of Science and Technology, Transaction A 30 : 165 – 174 .
  • Dixit , V. N. , Dewan , S. ( 1995 ). A note on quasi and bi-ideals in ternary semigroups . Internat. J. Math. & Math. Sci. 18 : 501 – 508 .
  • Dörnte , W. ( 1928 ). Untersuchungen über einen verallgemeinerten Gruppenbegriff . Math. Z. 29 : 1 – 19 .
  • Dudek , W. A. ( 2001 ). Idempotents in n-ary semigroups . Southeast Asian Bull. Math. 25 : 97 – 104 .
  • Dudek , W. A. ( 1980 ). Remarks on n-groups . Demonstratio Math. 13 : 165 – 181 .
  • Dudek , W. A. , Głazek, K. ( 2008 ). Around the Hosszú-Gluskin theorem for n-ary groups . Discrete Math. 308 : 4861 – 4876 .
  • Grzymala-Busse , J. W. (1969). Automorphisms of polyadic automata. J. Assoc. Comput. Mach. 16:208–219.
  • Kasner , E. ( 1904 ). An extension of the group concept . Bull. Amer. Math. Soc. 10 : 290 – 291 .
  • Kerner , R. ( 2000 ). Ternary Algebraic Structures and their Applications in Physics . Paris : Univ. P. and M. Curie .
  • Laywine , C. F. , Mullen , G. L. ( 1998 ). Discrete Mathematics Using Latin Squares . New York : Wiley .
  • Lehmer , D. H. ( 1932 ). A ternary analogue of abelian groups . Amer. J. Math. 59 : 329 – 338 .
  • Leoreanu-Fotea , V. , Davvaz , B. ( 2008 ). n-hypergroups and binary relations . European Journal of Combinatorics 29 : 1207 – 1218 .
  • Leoreanu-Fotea , V. , Davvaz , B. ( 2008 ). Roughness in n-ary hypergroups . Information Sciences 178 : 4114 – 4124 .
  • Los , J. ( 1995 ). On the extending of models I . Fundamenta Mathematicae 42 : 38 – 54 .
  • Marty , F. ( 1934 ). ur une generalization de la notion de group . Stockholm : 8th Congress Math. Scandenaves 45–49 .
  • Monk , D. , Sioson , F. M. ( 1966 ). m-semigroups, semigroups, function representations . Fund. Math. 59 : 233 – 241 .
  • Nikshych , D. , Vainerman , L. ( 2000 ). Finite Quantum Groupoids and Their Applications . Los Angeles : Univ. California .
  • Pojidaev , A. P. ( 2003 ). Enveloping algebras of Fillipov algebras . Comm. Algebra 31 : 883 – 900 .
  • Post , E. L. ( 1940 ). Polyadic groups . Trans. Amer. Math. Soc. 48 : 208 – 350 .
  • Rosenberg , I. G. ( 1998 ). Hypergroups and join spaces determined by relations . Italian Journal of Pure and Applied Mathematics 4 : 93 – 101 .
  • Rusakov , S. A. ( 1998 ). Some Applications of n-Ary Group Theory . Minsk : Belaruskaya navuka .
  • Sioson , F. M. ( 1965 ). Ideal theory in ternary semigroups . Math. Jpn. 10 : 63 – 84 .
  • Stojaković , Z. , Dudek , W. A. ( 1998 ). Single identities for varieties equivalent to quadruple systems Discrete Math. 183 : 277 – 284 .
  • Vainerman , L. , Kerner , R. ( 1996 ). On special classes of n-algebras . J. Math. Phys. 37 : 2553 – 2565 .
  • Vougiouklis , T. ( 1994 ). Hyperstructures and Their Representations . Palm Harbor , USA : Hadronic Press, Inc, p. 115 .
  • Communicated by V. A. Artamonov.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.