Locally equational completeness of rings and semigroups
M. R. Chiaro · Proceedings of the American Mathematical Society · 1977
Hu has developed locally equational classes as a generalization of equational classes. It is shown here that the lattice of equational classes of rings is a proper sublattice of the lattice of locally equational classes of rings but the locally equationally complete rings are precisely the equationally complete rings. Using the equational and locally equational class operators the locally equationally complete classes of semigroups are shown to be those that are equationally complete.