  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 un
preorder R. On this algebra we can consider one of the several binary
operations defined, in an abstract way, by A. Monteiro (1971). The
Heyting-Brouwer subalgebra of constants (fixpoints), allows us to give a
general framework to find representations of several special algebraic
structures related to logic.
