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2001 | 21 | 1 | 13-19
Tytuł artykułu

On exponentiation on n-ary hyperalgebras

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EN
Abstrakty
EN
For n-ary hyperalgebras we study a binary operation of exponentiation which to a given pair of n-ary hyperalgebras assigns their power, i.e., an n-ary hyperalgebra carried by the corresponding set of homomorphisms. We give sufficient conditions for the existence of such a power and for a decent behaviour of the exponentiation. As a consequence of our investigations we discover a cartesian closed subcategory of the category of n-ary hyperalgebras and homomorphisms between them.
Twórcy
  • Department of Mathematics, Technical University of Brno, 616 69 Brno, Czech Republic
  • Department of Mathematics, Technical University of Brno, 616 69 Brno, Czech Republic
Bibliografia
  • [1] J. Adámek, H. Herrlich, and G.E. Strecker, Abstract and Concrete Categories, John Wiley & Sons, New York 1990.
  • [2] R. Ameri and M.M. Zahedi, Hyperalgebraic systems, Italian J. Pure Appl. Math. 6 (1999), 21-32.
  • [3] P. Corsini, et al. (eds.), Algebraic Hyperstructures and Applications. Proceedings of the 6th International Congress, held in Prague 1996, Democritus University of Thrace, Alexandropolis 1997.
  • [4] J. Jezek and T. Kepka, Medial groupoids, Rozpravy CSAV, Rada Mat. a Prí rod. Ved., vol. 93, no.1, Academia, Prague 1983.
  • [5] J. P onka, Diagonal algebras, Fund. Math. 58 (1966), 309-321.
  • [6] I. Rosenberg, An algebraic approach to hyperalgebras, '6th IEEE International Symposium on Multiple-Valued Login' (Santiago de Compostela 1996), IEEE Computer Soc., Los Alamos 1996.
  • [7] I. Rosenberg, Multiple valued hyperstructures, '28th IEEE Proceedings of the Int. Symp. Multiple-Valued Logic,' (Fukuoka, Japan 1998), IEEE Computer Soc., Los Alamos CA, 1998, 326-333.
  • [8] J. Slapal, Exponentiality in concrete categories, New Zealand J. Math. 22 (1993), 87-90.
  • [9] J. Slapal, Direct arithmetic of relational systems, Publ. Math. (Debrecen) 38 (1991), 39-48.
  • [10] J. Slapal, On exponentiation of n-ary algebras, Acta Math. Hungar. 63 (1994), 313-322.
  • [11] J. Slapal, Cartesian closedness in categories of partial algebras, Math. Pannon. 7 (1996), 273-279.
  • [12] T. Vougiouklis, (ed.), Algebraic Hyperstructures and Applications, Proceedings of the Fourth International Congress, held at 'Demokritos' University of Trace, Xánthi, 1990, World Sci. Publ. Co., Teaneck, NY, 1991.
  • [13] M. Stefanescu, (ed.), Algebraic Hyperstructures and Applications, Proceedings of the Fifth International Congress held at 'Al. I Cuza' University, Iasi, 1993, Hadronic Press, Palm Harbor, FL, 1994.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1023
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