Related papers: Modularity prevents tails
We provide an affirmative answer for the question raised almost twenty years ago concerning the characterization of tilted artin algebras by the existence of a sincere finitely generated module which is not the middle of a short chain.
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…
We continue our study of ends of non-compact manifolds, with a focus on the inward tameness condition. For manifolds with compact boundary, inward tameness, has significant implications. For example, such manifolds have stable homology at…
We consider some distinguished classes of elements of a multiplicative lattice endowed with coarse lower topologies, and call them lower spaces. The primary objective of this paper is to study the topological properties of these lower…
By a twenty year old result of Ralph Freese, an $n$-element lattice $L$ has at most $2^{n-1}$ congruences. We prove that if $L$ has less than $2^{n-1}$ congruences, then it has at most $2^{n-2}$ congruences. Also, we describe the…
This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly…
We characterize those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruence preserving expansions.
Given a bounded lattice $L$ with bounds $0$ and $1$, it is well known that the set $\mathsf{Pol}_{0,1}(L)$ of all $0,1$-preserving polynomials of $L$ forms a natural subclass of the set $\mathsf{C}(L)$ of aggregation functions on $L$. The…
Let $\mathcal W$ be a nontrivial variety of lattices, and let $L$ be a finite lattice in $\mathcal W$. The congruence density of $L$ with respect to $\mathcal W$ is the number of congruences of $L$ divided by the maximum number of…
We prove completeness, interpolation and omitting types for certain predicate topological logics that properly extend the first order case. We aslo count the non isomorphic topological models of a countable theory
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…
For a slim, planar, semimodular lattice, G. Cz\'edli and E.\,T. Schmidt introduced the fork extension in 2012. In this note we prove that the fork extension has the Congruence Extension Property. This paper has been merged with Part II,…
We present a novel approach to the construction of new finite algebras and describe the congruence lattices of these algebras. Given a finite algebra $(B_0, \dots)$, let $B_1, B_2, \dots, B_K$ be sets that either intersect $B_0$ or…
We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the…
We give a natural extension of the notion of the contragredient module for a vertex operator algebra. By using this extension we prove that for regular vertex operator algebras, Zhu's $C_{2}$-finiteness condition holds, fusion rules are…
We provide a model theoretical and tree property like characterization of $\lambda$-$\Pi^1_1$-subcompactness and supercompactness. We explore the behaviour of those combinatorial principles at accessible cardinals.
To every minimal model of a complete local isolated cDV singularity Donovan--Wemyss associate a finite dimensional symmetric algebra known as the contraction algebra. We construct the first known standard derived equivalences between these…
Two observations in support of the thesis that trusses are inherent in ring theory are made. First, it is shown that every equivalence class of a congruence relation on a ring or, equivalently, any element of the quotient of a ring $R$ by…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.
The congruence orbit of a matrix has a natural connection with the linear complementarity problem on simplicial cones formulated for the matrix. In terms of the two approaches -- the congruence orbit and the family of all simplicial cones…