On exponentiation on n-ary hyperalgebras

František Bednařík; Josef Šlapal

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 1, page 13-19
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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František Bednařík, and Josef Šlapal. "On exponentiation on n-ary hyperalgebras." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 13-19. <http://eudml.org/doc/287598>.

@article{FrantišekBednařík2001,
abstract = {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.},
author = {František Bednařík, Josef Šlapal},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {n-ary hyperalgebra; medial hyperalgebra; diagonalhyperalgebra; power of hyperalgebras; cartesian closed category; -ary hyperalgebras; exponentiation},
language = {eng},
number = {1},
pages = {13-19},
title = {On exponentiation on n-ary hyperalgebras},
url = {http://eudml.org/doc/287598},
volume = {21},
year = {2001},
}

TY - JOUR
AU - František Bednařík
AU - Josef Šlapal
TI - On exponentiation on n-ary hyperalgebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 13
EP - 19
AB - 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.
LA - eng
KW - n-ary hyperalgebra; medial hyperalgebra; diagonalhyperalgebra; power of hyperalgebras; cartesian closed category; -ary hyperalgebras; exponentiation
UR - http://eudml.org/doc/287598
ER -

References

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  8. [8] J. Slapal, Exponentiality in concrete categories, New Zealand J. Math. 22 (1993), 87-90. Zbl0793.18004
  9. [9] J. Slapal, Direct arithmetic of relational systems, Publ. Math. (Debrecen) 38 (1991), 39-48. Zbl0733.08001
  10. [10] J. Slapal, On exponentiation of n-ary algebras, Acta Math. Hungar. 63 (1994), 313-322. Zbl0798.08001
  11. [11] J. Slapal, Cartesian closedness in categories of partial algebras, Math. Pannon. 7 (1996), 273-279. Zbl0858.08003
  12. [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. [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. 

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