Modularity and distributivity of tolerance lattices of commutative inverse semigroups
Bedřich Pondělíček · Czechoslovak Mathematical Journal · 1985
By a tolerance on an algebra Ä we mean a reflexive and symmetric subalgebra of the direct product Ä x Ä.The set Т(Л) of all tolerances on Ä forms a complete algebraic lattice with respect to set inclusion (xee [l] and [2]).In the present paper we give a description of a commutative inverse semigroup S whose lattice T(S) of tolerances is modular or distributive.Notice that S is found to be an algebra with a multiplication and a unary operation of inverse (see part III of [3]). MODULARITY AND DISTRIBUTIVITY