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Discussiones Mathematicae General Algebra and Applications 21(1) (2001) 13-19
DOI: https://doi.org/10.7151/dmgaa.1023

ON EXPONENTIATION OF n-ARY HYPERALGEBRAS

Frantisek Bednarík and Josef Slapal

Department of Mathematics, Technical University of Brno
616 69 Brno, Czech Republic
e-mail: slapal@kinf.fme.vutbr.cz

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.

Keywords: n-ary hyperalgebra, medial hyperalgebra, diagonalhyperalgebra, power of hyperalgebras, cartesian closed category.

2000 Mathematics Subject Classification: 08A99, 08C05.

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Received 16 March 1999