Abstract
The graph of an algebra A is the relational structure G(A) in which the relations are the graphs of the basic operations of A. Let denote by the class of all graphs of algebras from a class . We prove that if is a class of semigroups possessing a nontrivial member with a neutral element, then does not have finite quasi-equational basis. We deduce that, for a class of monoids or groups with a nontrivial member, also does not have finite quasi-equational basis.
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Communicated by Mikhail Volkov.
The author was supported by the Eduard Čech Center Grant LC505 and by the Statutory Grant of Warsaw University of Technology 504G11200112000.
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Stronkowski, M.M. Quasi-equational bases for graphs of semigroups, monoids and groups. Semigroup Forum 82, 296–306 (2011). https://doi.org/10.1007/s00233-010-9268-4
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DOI: https://doi.org/10.1007/s00233-010-9268-4