In this paper we define, inspired by ring theory, the class of maximal residuated lattices with lifting Boolean center and prove a structure theorem for them: any maximal residuated lattice with lifting Boolean center is isomorphic to a finite direct product of local residuated lattices. MSC: 06F35, 03G10.

The employment of proper codings, such as the base-2 coding, has allowed to establish the universal approximation property of Boolean functions: if a sufficient number b of inputs (bits) is taken, they are able to approximate arbitrarily well any real Borel measurable mapping. However, if the reduced set of monotone Boolean functions, whose expression involves only and and or operators, is cons...

In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.

We construct a diagram D⊲⊳, indexed by a finite partially ordered set, of finite Boolean 〈∨, 0, 1〉-semilattices and 〈∨, 0, 1〉-embeddings, with top semilattice 2, such that for any variety V of algebras, if D⊲⊳ has a lifting, with respect to the congruence lattice functor, by algebras and homomorphisms in V, then there exists an algebra U in V such that the congruence lattice of U contains, as a...

In this paper we shall give a topological duality for Boolean algebras endowed with an n-ary monotonic operator (BAMOs). The dual spaces of BAMOs are structures of the form ⟨X,R, τ⟩, such that ⟨X, τ⟩ is a Boolean space, and R is a relation between X and finite sequences of non-empty closed subsets of X. By means of this duality we shall characterize the equivalence relations of the dual space o...

We initiate a study of topological orthoalgebras (TOAs), concentrating on the compact case. Examples of TOAs include topological orthomodular lattices, and also the projection lattice of a Hilbert space. As the latter example illustrates, a lattice-ordered TOA need not be a topological lattice. However, we show that a compact Boolean TOA is a topological Boolean algebra. Using this, we prove th...

Let L be a finite lattice and let L̂ = L − {0̂, 1̂}. It is shown that if the order complex ∆(L̂) satisfies H̃k−2 ( ∆(L̂) ) 6= 0 then |L| ≥ 2k. Equality |L| = 2k holds iff L is isomorphic to the Boolean lattice {0, 1}k.

It is known that a (concept) lattice contains an n-dimensional Boolean suborder if and only the context contra-nominal scale as subcontext. In this work, we investigate more closely interplay between subcontexts of given finite suborders its concept lattice. To end, define mappings from set to vice versa study their structural properties. addition, introduce closed-subcontexts extension closed ...

We find the excluded minors for minor-closed class of lattice path polymatroids as a subclass Boolean polymatroids. Like matroids and polymatroids, there are infinitely many minors, but they fall into small number easily-described types.

Realistic 3D-conformations of protein structures can be embedded in a cubic lattice using exclusively integer numbers, additions, subtractions and boolean operations.