Publication at Faculty of Mathematics and Physics |
2011
Abstract
The graph of an algebra is defined as a relational structure that consists of the graphs induced by all basic operation. The paper is concerend with the questione whether there exists a finite basis of quasi-identities for the quasivariety that is generated by graphs of a given class of algebras.
It is proved that no such basis exists if the class consists of semigroups one of which is a nontrivial semigroup that possesses a neutral element. The same result is true for a nontrivial class of monoids or groups.