Related papers: Formal Concepts and Residuation on Multilattices
We give a sharp upper bound on the multiplicity of a fake weighted projective space with at worst canonical singularities. This is equivalent to giving a sharp upper bound on the index of the sublattice generated by the vertices of a…
The aim of this paper is to study lattice properties of the sharp partial order for complex matrices having index at most 1. We investigate the down-set of a fixed matrix $B$ under this partial order via isomorphisms with two different…
We study the existence of nontrivial and of representable (dual) weak complementations, along with the lattice congruences that preserve them, in different constructions of bounded lattices, then use this study to determine the finite…
The set of all transformation monoids on a fixed set of infinite cardinality \lambda, equipped with the order of inclusion, forms a complete algebraic lattice Mon(\lambda) with 2^{\lambda} compact elements. We show that this lattice is…
It was proved by Maksimova in 1977 that exactly eight varieties of Heyting algebras have the amalgamation property, and hence exactly eight axiomatic extensions of intuitionistic propositional logic have the deductive interpolation…
Since the invention of the famous LLL algorithm, lattice reduction has been an extremely useful tool in computational number theory. By construction, the LLL algorithm deals with lattices living in a vector space endowed with a positive…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
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…
The collection CL(T) of nonempty convex sublattices of a lattice T ordered by bi-domination is a lattice. We say that T has the fixed point property for convex sublattices (CLFPP for short) if every order preserving map f from T to CL(T)…
In this paper, we introduce the concept of residuated implications derived from quasi-overlap functions on lattices and prove some related properties. In addition, we formalized the residuation principle for the case of quasi-overlap…
A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…
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;…
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…
For many equation-theoretical questions about modular lattices, Hall and Dilworth give a useful construction: Let $L_0$ be a lattice with largest element $u_0$, $L_1$ be a lattice disjoint from $L_0$ with smallest element $v_1$, and $a \in…
Let $\mathcal{O}$ be a Dedekind domain whose field of fractions $K$ is a global field. Let $A$ be a finite-dimensional separable $K$-algebra and let $\Lambda$ be an $\mathcal{O}$-order in $A$. Let $n$ be a positive integer and suppose that…
Unitally nondistributive quantales are unital quantales such that the unit is approximable by the totally below relation and does not meet-distribute over arbitrary joins. It is shown that the underlying nondistributive complete lattice…
Stone-type dualities provide a powerful mathematical framework for studying properties of logical systems. They have recently been fruitfully explored in understanding minimisation of various types of automata. In Bezhanishvili et al.…
The purpose of this article is to propose and investigate a partial order structure weaker than the lattice structure and which have nice properties regarding closure operators. We extend accordingly closed pattern mining and formal concept…
The concept of a sectionally pseudocomplemented lattice was introduced by I. Chajda as an extension of relative pseudocomplementation for not necessarily distributive lattices. The typical example of such a lattice is the non-modular…
Pseudo-effect algebras are partial algebraic structures, that were introduced as a non-commutative generalization of effect algebras. In the present paper, lattice ordered pseudo-effect algebras are considered as possible algebraic…