Hyperidentities



L.P., On hyperassociativity, Algebra Universalis, 36 (1996), 363-378
 
The paper shows that the identities $x^4 = x^2, xyxzxyx = xyzyx, xy^2z^2 = xyz^2yz^2$ and $x^2y^2z = x^2yx^2yz$ form an equational basis of $\bold H$, the largest hyperassociative variety of semigroups. We present here a model of the free algebra in $\bold H$ on 2 generators (it has 94 elements) and solve the word problem for completely regular part of the free algebra in $\bold H$ with any number of generators.


L.P., All solid varieties of semigroups, Journal of Algebra 219 (1999), 421-436

Abstract : A solid variety is a variety in which every identity holds as a hyperidentity that is, we substitute not only elements for the variables but also term operations for the operational symbols. There are obvious necessary conditions for a variety of semigroups to be solid. We will show here that these conditions are also sufficient.