Related papers: Unification on subvarieties of pseudocomplemented …
In \cite[Rem. 3.4]{DNO} the authors asked the question if any \'etale subalgebra of an \'etale algebra in a braided fusion category is also \'etale. We give a positive answer to this question if the braided fusion category $\cc$ is…
We give several characterizations of discrete Sugeno integrals over bounded distributive lattices, as particular cases of lattice polynomial functions, that is, functions which can be represented in the language of bounded lattices using…
Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…
Gr\"atzer and Lakser asked in the 1971 {\sl Transactions of the American Mathematical Society} if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by ${\bf 2}^n\oplus{\bf 1}$ can be…
For an ordered array of critical volatile wetting droplets the formation of a super lattice by an Ostwald-ripening like competition process is considered. The underlying diffusion problem is treated within a quasistatic approximation and to…
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…
We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.
We prove that the lattice of normal subgroups of ultraproducts of compact simple non-abelian groups is distributive. In the case of ultraproducts of finite simple groups or compact connected simple Lie groups of bounded rank the set of…
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 consider abelian length categories, a generalization of module categories over Artin algebras. Let $\mathcal{A}$ be an abelian length category of colocal type. We show that the lattice $\mathsf{S}(\mathcal{A})$ of full additive subobject…
We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the…
Categories enriched over a commutative unital quantale can be studied as generalized, or many-valued, ordered structures. Because many concepts, such as complete distributivity, in lattice theory can be characterized by existence of certain…
In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal congruences in…
We first construct explicit bases for the cotangent spaces at singular points on Hibi toric varieties, i.e., toric varieties associated to distributive lattices. We then determine the singular loci of these toric varieties.
In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the…
We propose an algebraic and a geometric classification of euclidean isodual lattices of fixed rank. First, we prove that these lattices are distribued according to a finite number of algebraic types. Second, we show that they are…
We classify discrete quantum subgroups in the quantum double of the $q$-deformation of a compact semisimple Lie group, regarded as the complexification. We also record their classifications in some variants of quantum groups. Along the way,…
We characterize the finite intervals of the Muchnik lattice by proving that they are a certain proper subclass of the finite distributive lattices.
The symmetry approach is used for classification of integrable isotropic vector Volterra lattices on the sphere. The list of integrable lattices consists mainly of new equations. Their symplectic structure and associated PDE of vector…
In this paper, a subclass of bounded distributive lattices, that is, finitely disjunctive distributive lattices (FDD-lattices) have been introduced. Then we apply it to establish a Stone duality for Lawson compact algebraic L-domains.…