Related papers: Left-continuous pseudo-t-norms on modular lattices
We construct a complete lattice $Z$ such that the binary supremum function $\sup:Z\times Z\to Z$ is discontinuous with respect to the product topology on $Z\times Z$ of the Scott topologies on each copy of $Z$. In addition, we show that…
Defects in the atomic lattice of solids are sometimes desired. For example, atomic vacancies, single ones or more elaborated defective structures, can generate localized magnetic moments in a non magnetic crystalline lattice. Increasing…
The uninorms with continuous underlying t-norm and t-conorm are characterized via an extended ordinal sum construction. Using the results of [18], where each uninorm with continuous underlying operations was characterized by properties of…
In an earlier paper, to describe how a congruence spreads from a prime interval to another in a finite lattice, I introduced the concept of prime-perspectivity and its transitive extension, prime-projectivity and proved the…
Weakly orthomodular and dually weakly orthomodular lattices were introduced by the authors in a recent paper. Similarly as for orthomodular lattices we try to introduce an implication in these lattices which can be easily axiomatized and…
We illustrate some problems that are related to the existence of an underlying linear structure at the level of the property lattice associated with a physical system, for the particular case of two explicitly separated spin 1/2 objects…
We characterize well-founded algebraic lattices by means of forbidden subsemilattices of the join-semilattice made of their compact elements. More specifically, we show that an algebraic lattice $L$ is well-founded if and only if $K(L)$,…
We initiate in this article the study of weakly exact structures, a generalization of Quillen exact structures. We introduce weak counterparts of one-sided exact structures and show that a left and a right weakly exact structure generate a…
The sets of all neutral, distributive and lower-modular elements of the lattice of semigroup varieties are finite, countably infinite and uncountably infinite, respectively. In 2018, we established that there are precisely three neutral…
Let $L$ be a finite lattice and let $I$ be an ideal of $L$. Then the restriction map is a bounded lattice homomorphism of the congruence lattice of~$L$ into the congruence lattice of $I$. In a 2009 paper, the authors proved the converse. In…
In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one components, namely interlaced solitons. These are waveforms in which in the relevant anti-continuum limit, i.e.…
We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them,…
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 present a streamlined and (hopefully) accessible proof of the model-completeness of the weak monadic second order version of a dense linear order with left-endpoint but no right-endpoint in a particular finite signature. We also show how…
We define a new structure on a space endowed with convexities, and call it a fractoconvex structure (or, a space with fractoconvexity). We introduce two operations on a set of fractoconvexities and in a special case we show that they…
Distributive skew lattices satisfying $x\wedge (y\vee z)\wedge x = (x\wedge y\wedge x) \vee (x\wedge z\wedge x)$ and its dual are studied, along with the larger class of linearly distributive skew lattices, whose totally preordered…
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 investigate the alternate order on a congruence-uniform lattice $\mathcal{L}$ as introduced by N. Reading, which we dub the core label order of $\mathcal{L}$. When $\mathcal{L}$ can be realized as a poset of regions of a simplicial…
The methods to classify extremal unimodular lattices with given automorphisms are extended to the situation of modular lattices. A slightly more general notion than the type from the PhD thesis of Michael Juergens is the det-type. The…
The systematic study of planar semimodular lattices started in 2007 with a series of papers by G. Gr\"atzer and E. Knapp. These lattices have connections with group theory and geometry. A planar semimodular lattice $L$ is {\it slim} if…