Related papers: On PBZ*-lattices
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…
In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking…
In this paper we show that several classes of partially ordered structures having paraorthomodular reducts, or whose sections may be regarded as paraorthomodular posets, admit a quite natural notion of implication, that admits a suitable…
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…
We complete the study of characters on higher rank semisimple lattices initiated in [BH19,BBHP20], the missing case being the case of lattices in higher rank simple algebraic groups in arbitrary characteristics. More precisely, we…
We study the structure of bounded simple weight $\mathfrak{sl}(\infty)$-, $\mathfrak{o}(\infty)$-, $\mathfrak{sp}(\infty)$-modules, which have been recently classified in [6]. Given a splitting parabolic subalgebra $\mathfrak{p}$ of…
Motivated by work of Barot, Geiss and Zelevinsky, we study a collection of Z-bases (which we call companion bases) of the integral root lattice of a root system of simply-laced Dynkin type. Each companion basis is associated with the quiver…
A natural first step in the classification of all `physical' modular invariant partition functions $\sum N_{LR}\,\c_L\,\C_R$ lies in understanding the commutant of the modular matrices $S$ and $T$. We begin this paper extending the work of…
Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
A planar semimodular lattice $L$ is \emph{slim} if $\mathbf{M}_3$ is not a sublattice of $L$. In a recent paper, G. Cz\'edli introduced a very powerful diagram type for slim, planar, semimodular lattices. This short note proves the…
We study varieties generated by semi-primal lattice-expansions by means of category theory. We provide a new proof of the Keimel-Werner topological duality for such varieties and, using similar methods, establish its discrete version. We…
For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
We define and study semilattices and lattices for $E$-closed families of theories. Properties of these semilattices and lattices are investigated. It is shown that lattices for families of theories with least generating sets are…
We give a classification of the lattices of rank r=4, r=8 and r=12 over \Q(\sqrt{-3}), which are even and unimodular \Z-lattices. Using this classification we construct the associated theta series, which are Hermitian modular forms, and…
In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…
A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach, we give explicit vertex operator construction of certain indecomposable and logarithmic modules for the…
In this paper, we first classify all irreducible modules of the vertex algebra $V_L^+$ when $L$ is a negative definite even lattice of arbitrary rank. In particular, we show that any irreducible $V_L^+$-module is isomorphic to a submodule…
In 1986, Oliver Pretzel studied the set of orientations of a connected finite graph $G$ and showed that any two such orientations having the same flow-difference around all closed loops can be obtained from one another by a succession of…