Related papers: Congruence Boolean Lifting Property
In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in…
For a locally convex $^*$-algebra $A$ equipped with a fixed continuous $^*$-character $\varepsilon$, we define a cohomological property, called property $(FH)$, which is similar to character amenability. Let $C_c(G)$ be the space of…
We study the question which Boolean algebras have the property that for every generating set there is an ultrafilter selecting maximal number of its elements. We call it the ultrafilter selection property. For cardinality aleph-one the…
Each quiver corresponds to a path semigroup, and such a path semigroup also corresponds to an associative K-algebra over an algebraically closed field K. Let Q be a quiver and S_Q, KQ be its path semigroup, path algebra, respectively. In…
Inspired by the ideas and techniques used in the study of cluster algebras we construct a new class of algebras, called bistellar cluster algebras, from closed oriented triangulated even-dimensional manifolds by performing…
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground…
We observe that many of the separation axioms of topology (including $T_0-T_4$) can be expressed concisely and uniformly in terms of category theory as lifting properties (in the sense of Quillen model categories) with respect to (usually…
In analogy with the C*-algebra theory, we study variants appropriate to nonselfadjoint algebras of nuclearity, the local lifting property, exactness, and the weak expectation property. In addition, we study the relationships between these…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizeable; that is, if all 2-generated subalgebras are…
The problem of learning from label proportions (LLP) involves training classifiers with weak labels on bags of instances, rather than strong labels on individual instances. The weak labels only contain the label proportion of each bag. The…
We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\lambda_s$ (the algebraic convergence) and $\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov…
In this paper, we discuss a property of the Kullback--Leibler divergence measured between two models of the family of the location-scale distributions. We show that, if model $M_1$ and model $M_2$ are represented by location-scale…
Ladders of recollements of abelian categories are introduced, and used to address three general problems. Ladders of a certain height allow to construct recollements of triangulated categories, involving derived categories and singularity…
The category $\mathbb{DRDL'}$, whose objects are c-differential residuated distributive lattices that satisfy the condition $\mathbf{CK}$, is the image of the category $\mathbb{RDL}$, whose objects are residuated distributive lattices,…
We prove that every distributive algebraic lattice with at most $\aleph\_1$ compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The $\aleph\_1$ bound is optimal, as…
We apply the super duality formalism recently developed by the authors to obtain new equivalences of various module categories of general linear Lie superalgebras. We establish the correspondence of standard, tilting, and simple modules, as…
We derive relations between theoretical properties of restricted Boltzmann machines (RBMs), popular machine learning models which form the building blocks of deep learning models, and several natural notions from discrete mathematics and…
We present a family of local involutive integral bounded residuated lattice-ordered commutative monoids (involutive residuated lattices, for short) having Boolean term, radical term (see \cite{CT12} and \cite{T23}), and satisfying GAP…
For given Boolean algebras $\mathbb{A}$ and $\mathbb{B}$ we endow the space $\mathcal{H}(\mathbb{A},\mathbb{B})$ of all Boolean homomorphisms from $\mathbb{A}$ to $\mathbb{B}$ with various topologies and study convergence properties of…