Filter theory of bounded residuated lattice ordered monoids

Abstract

Bounded residuated lattice ordered monoids (R -monoids) are a common generalization of pseudo-BL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. In the paper we introduce and study classes of filters of bounded R -monoids leading (in normal cases) to quotient algebras which are Heyting algebras, Boolean algebras and GMV-algebras (=pseudo-MV-algebras), respectively.