Claudia Mureşan

Generalized Bosbach states: Part II

We continue the investigation of generalized Bosbach states that we began in Part I, restricting our research to the commutative case and treating further aspects related to these states. Part II is concerned with similarity convergences, continuity of states and the construction of the s-completion of a commutative residuated lattice, where s is a generalized Bosbach state.

Boolean lifting property for residuated lattices

In this paper we define the Boolean lifting property (BLP) for residuated lattices to be the property that all Boolean elements can be lifted modulo every filter, and study residuated lattices with BLP. Boolean algebras, chains, local and hyperarchimedean residuated lattices have BLP. BLP behaves interestingly in direct products and involutive residuated lattices, and it is closely related to arithmetic properties involving Boolean elements, nilpotent elements and elements of the radical. When BLP is present, strong representation theorems for semilocal and maximal residuated lattices hold.

Boolean Lifting Properties for Bounded Distributive Lattices

In this paper, we introduce the lifting properties for the Boolean elements of bounded distributive lattices with respect to the congruences, filters and ideals, we establish how they relate to each other and to significant algebraic properties, and we determine important classes of bounded distributive lattices which satisfy these lifting properties.

Algebraic and topological results on lifting properties in residuated lattices

We define lifting properties for universal algebras, which we study in this general context and then particularize to various such properties in certain classes of algebras. Next we focus on residuated lattices, in which we investigate lifting properties for Boolean and idempotent elements modulo arbitrary, as well as specific kinds of filters. We give topological characterizations to the lifting property for Boolean elements and several properties related to it, many of which we obtain by means of the reticulation.

Co-stone Residuated Lattices

In this paper we present some applications of the reticulation of a residuated lattice, in the form of a transfer of properties between the category of bounded distributive lattices and that of residuated lattices through the reticulation functor. The results we are presenting are related to co-Stone algebras; among other applications, we transfer a known characterization of

Factor Congruence Lifting Property

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Dense Elements and Classes of Residuated Lattices

-co-Stone bounded distributive lattices to residuated lattices and we prove that the reticulation functor for residuated lattices preserves the strongly co-Stone hull.

The Reticulation of a Residuated Lattice

In previous work, we have introduced and studied a lifting property in congruence–distributive universal algebras which we have defined based on the Boolean congruences of such algebras, and which we have called the Congruence Boolean Lifting Property. In a similar way, a lifting property based on factor congruences can be defined in congruence–distributive algebras; in this paper we introduce and study this property, which we have called the Factor Congruence Lifting Property. We also define the Boolean Lifting Property in varieties with

Maximal residuated lattices with lifting boolean center

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