Related papers: Quasicomplemented residuated lattices
The notion of $n$-normal residuated lattice, as a class of residuated lattices in which every prime filter contains at most $n$ minimal prime filters, is introduced and studied. Before that, the notion of $\omega$-filter is introduced and…
We develop the theory of residuated lattices by introducing and studying several new types of filters and related concepts, including semi-simple filters, essential filters, the socle of a filter, and independent families of filters. Our…
It is known that every relatively pseudocomplemented lattice is residuated and, moreover, it is distributive. Unfortunately, non-distributive lattices with a unary operation satisfying properties similar to relative pseudocomplementation…
M.S. Rao recently investigated some sorts of special filters in distributive pseudocomplemented lattices. In our paper we extend this study to lattices which need neither be distributive nor pseudocomplemented. For this sake we define a…
In this paper, we introduce the notion of a pseudo-irreducible filter in a residuated lattice and compare this concept with related notions such as prime and maximal filters. Then, we recall the Boolean lifting property for filters and…
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by a\rightarrow b and can be considered as the connective…
The aim of this paper is to study the class of quasicomplemented distributive nearlattices. We investigate $\alpha$-filters and $\alpha$-ideals in quasicomplemented distributive nearlattices and some results on ideals-congruence-kernels.…
In this paper we study the dense elements and the radical of a residuated lattice, residuated lattices with lifting Boolean center, simple, local, semilocal and quasi-local residuated lattices. BL-algebras have lifting Boolean center;…
This paper is devoted to the study of a fascinating class of residuated lattices, the so-called mp-residuated lattice, in which any prime filter contains a unique minimal prime filter. A combination of algebraic and topological methods is…
In this paper, a combination of algebraic and topological methods is applied to obtain new and structural results on Gelfand residuated lattices. It is demonstrated that Gelfand's residuated lattices strongly tied up with the hull-kernel…
Residuated lattices play an important role in the study of fuzzy logic based of t-norm. In this paper, we introduced the notions of n-fold implicative filters, n-fold positive implicative filters, n-fold boolean filters, n-fold fantastic…
A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which…
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…
We study systems that approach a state possessing discrete symmetry due to different degenerate realizations for the system. For concreteness, we consider fractionally filled systems where degeneracy comes from the presence of identical…
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…
We show that all balanced d-lattices must be complemented, answering a question of Chajda and Eigenthaler. (A bounded lattice is balanced if any two congruences agree on their 1-classes iff they agree on their 0-classes.) Our main tool is…
We characterize commutative idempotent involutive residuated lattices as disjoint unions of Boolean algebras arranged over a distributive lattice. We use this description to introduce a new construction, called gluing, that allows us to…
We characterize those semilattices that give rise to Boolean spaces on their associated spaces of ultrafilters. The class of 0-disjunctive semilattices, important in the theory of congruence-free inverse semigroups, plays a distinguished…
We survey the state of the art on amalgamation in varieties of semilinear residuated lattices. Our discussion emphasizes two prominent cases from which much insight into the general picture may be gleaned: idempotent varieties and their…
We introduce the concept of a quasiresiduated lattice and prove that every lattice effect algebra can be organized into a commutative quasiresiduated lattice with divisibility. Also conversely, every such a lattice can be converted into a…