Semigroup Forum

, Volume 82, Issue 2, pp 296–306 | Cite as

Quasi-equational bases for graphs of semigroups, monoids and groups

Open Access
Research Article

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 Open image in new window the class of all graphs of algebras from a class Open image in new window. We prove that if Open image in new window is a class of semigroups possessing a nontrivial member with a neutral element, then Open image in new window does not have finite quasi-equational basis. We deduce that, for a class Open image in new window of monoids or groups with a nontrivial member, Open image in new window also does not have finite quasi-equational basis.

Keywords

Graphs of semigroups Finite axiomatizability Finite quasi-equational bases Quasivarieties of relational structures 

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  1. 1.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland
  2. 2.Eduard Čech CenterCharles UniversityPragueCzech Republic

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