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Weakening Relation Algebras And Fl2-Algebras, Nikolaos Galatos, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

FL²-algebras are lattice-ordered algebras with two sets of residuated operators. The classes RA of relation algebras and GBI of generalized bunched implication algebras are subvarieties of FL²-algebras. We prove that the congruences of FL²-algebras are determined by the congruence class of the respective identity elements, and we characterize the subsets that correspond to this congruence class. For involutive GBI-algebras the characterization simplifies to a form similar to relation algebras.

For a positive idempotent element p in a relation algebra A, the double division conucleus image p/A/p is an (abstract) weakening relation algebra, …