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Inspired by the fundamental results obtained by P. Halmos and A. Monteiro,concerning equivalence relations and monadic Boolean algebras, we recall the`concrete' Rauszer Boolean algebra pointed out by C. Rauszer (1971), via unpreorder R. On this algebra we can consider one of the several binaryoperations defined, in an abstract way, by A. Monteiro (1971). TheHeyting-Brouwer subalgebra of constants (fixpoints), allows us to give ageneral framework to find representations of several special algebraicstructures related to logic.

About a 'concrete' Rauszer Boolean algebra generated by a preorder