Abstract
The paper shows that the identitiesx 4 x 2,xyxzxyx xyzyx, xy 2 z 2 xyz 2 yz 2 andx 2 y 2 z x 2 yx 2 yz form an equational basis of H, the largest hyperassociative variety of semigroups. We present here a model of the free algebra in H on 2 generators (it has 94 elements) and solve the word problem for completely regular part of the free algebra in H with any number of generators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Denecke, K. andKoppitz, J.,Hyperassociative varieties of semigroups, Semigroup Forum49 (1994), 41–48.
Denecke, K., Lau, D., Pöschel, R. andSchweigert, D.,Hyperidentities, hyperequational classes and clone congruences, Contribution to General Algebra7 (1991), 97–118.
Denecke, K. andWismath, S.,Solid varieties of semigroups, Semigroup Forum48 (1994), 219–234.
Koppitz, J.,On equational description of solid semigroup varieties, preprint.
Schweigert, D.,Hyperidentities, inAlgebras and Orders (ed. I. G. Rosenberg and G. Sabidussi), Kluwer Academic Publishers, 1993, 405–506.
Author information
Authors and Affiliations
Additional information
The author acknowledges the support of the Grant no. 201/93/2121 of the Grant Agency of Czech Republic. The main part of research was carried out during the author's visit to Prof. I. G. Rosenberg at the University of Montreal within the NATO Collaborative Grant no. LG 930 302.
Rights and permissions
About this article
Cite this article
Polák, L. On hyperassociativity. Algebra Universalis 36, 363–378 (1996). https://doi.org/10.1007/BF01236762
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01236762