The Belluce-semilattice associated with a monadic residuated lattice.

The aim of this paper was to study the Belluce-semilattice associated with a monadic residuated lattice. Some characterizations of ∩ -prime monadic filters and maximal monadic filters are derived, respectively. The ∩ -prime monadic filter theorem is also established. The relationships among strong monadic filters, ∩ -prime monadic filters, prime monadic filters and maximal monadic filters are discussed. It is proven that there are monadic residuated lattices having no prime monadic filters and that ∩ -prime monadic filters and prime monadic filters coincide in strong monadic residuated lattices. We consider the Belluce-semilattice associated with a monadic residuated lattice and demonstrate that the Belluce-semilattice associated with a monadic residuated lattice (a strong monadic residuated lattice) is a bounded distributive meet-semilattice (lattice). The homeomorphism between ∩ -prime monadic filter space of a monadic residuated lattice and ∩ -prime filter space of its Belluce-semilattice is obtained. In addition, we derive that there is a meet-semilattice isomorphism between the Belluce-semilattices associated with a monadic residuated lattice and its underlying m-relatively complete subalgebra. [ABSTRACT FROM AUTHOR]