Related papers: Integrally Closed Residuated Lattices
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
A lattice-theoretic framework is introduced that permits the study of the conditional independence (CI) implication problem relative to the class of discrete probability measures. Semi-lattices are associated with CI statements and a…
We show that every complemented modular lattice can be converted into a left residuated lattice where the binary operations of multiplication and residuum are term operations. The concept of an operator left residuated poset was introduced…
In this paper, the class of quasicomplemented residuated lattices is introduced and investigated, as a subclass of residuated lattices in which any prime filter not containing any dense element is a minimal prime filter. The notion of…
It is known from Grzegorczyk's paper \cite{grze-1951} that the lattice of real semi-algebraic closed subsets of ${\mathbb R}^n$ is undecidable for every integer $n\geq 2$. More generally, if $X$ is any definable set over a real or…
One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…
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…
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…
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…
Let $G$ be a real centre-free semisimple Lie group without compact factors. I prove that irreducible lattices in $G$ are rigid under two types of sublinear distortions. The first result is that the class of lattices in groups that do not…
In this paper, we characterize the congruences of an arbitrary i--lattice, investigate the structure of the lattice they form and how it relates to the structure of the lattice of lattice congruences, then, for an arbitrary non--zero…
In this paper we study projective algebras in varieties of (bounded) commutative integral residuated lattices from an algebraic (as opposed to categorical) point of view. In particular we use a well-established construction in residuated…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
Distributive Stonean residuated lattices are closely related to Stone algebras since their bounded lattice reduct is a Stone algebra. In the present work we follow the ideas presented by Chen and Gr\"{a}tzer and try to apply them for the…
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…
We show that every orthomodular lattice can be considered as a left residuated l-groupoid satisfying divisibility, antitony, the double negation law and three more additional conditions expressed in the language of residuated structures.…
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…
The congruence lattices of all algebras defined on a fixed finite set $A$ ordered by inclusion form a finite atomistic lattice $\mathcal E$. We describe the atoms and coatoms. Each meet-irreducible element of $\mathcal E$ being determined…
Multidimensional consistency has emerged as a key integrability property for partial difference equations (P$\Delta$Es) defined on the "space-time" lattice. It has led, among other major insights, to a classification of scalar affine-linear…
Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…