Quasi-equational bases for graphs of semigroups, monoids and groups.
The graph of an algebra \(\mathbf A\) is the relational structure \(G(\mathbf A)\) in which the relations are the graphs of the basic operations of \(\mathbf A\). Denote by \(G(\mathcal K)\) the class of all graphs of algebras from a class \(\mathcal K\). The author proves that if \(\mathcal K\) is a class of semigroups possessing a nontrivial member with a neutral element, then \(G(\mathcal K)\) does not have finite quasi-equational bases. As a corollary of this result, a similar result for a nontrivial class \(\mathcal K\) of monoids or groups is received. For contrast the author marks, that if \(\mathcal K\) is a nontrivial class of semigroups with zero multiplication, then the class \(G(\mathcal K)\) has a quasi-equational basis consisting of two quasi-identities.
scientific article; zbMATH DE number 5886837