相关论文: Taylor is prime
We study the Hobby-McKenzie varieties that constitute a major class investigated thoroughly in the monograph The shape of congruence lattices by Kearnes and Kiss. We obtain new characterizations of the Hobby-McKenzie varieties via…
We give a combinatorial proof that congruence permutability is prime in the lattice of interpretability types of varieties. Thereby, we settle a 1984 conjecture of Garcia and Taylor.
We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.
We prove that for all $n$, simultaneously, we can choose prime filtrations of $R/I^n$ such that the set of primes appearing in these filtrations is finite.
We show that all balanced d-lattices must be complemented, answering a question of Chajda and Eigenthaler. (A bounded lattice is balanced if any two congruences agree on their 1-classes iff they agree on their 0-classes.) Our main tool is…
We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…
We study sigma-ideals and regularity properties related to the "filter-Laver" and "dual-filter-Laver" forcing partial orders. An important innovation which enables this study is a dichotomy theorem proved recently by Miller [1]. [1] Arnold…
Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…
A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and denominators are fixed. In one variable, Taylor varieties are given by rank constraints on…
We review the notion of (finitary) filter pair as a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
We elaborate on the notion of a filtration of an operad defined in terms of a lattice-valued operad serving as an indexing object. That covers ordinary integer-indexed filtrations of associative algebras and operads as a special case, yet…
We provide a partial result on Taylor's modularity conjecture, and several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and we…
In this paper, we introduce the concept of filter on IL-algebra. It is proved that this concept generalizes the notion of filter on Residuated Lattices. Prime filters on IL-algebra are defined and few interesting properties are obtained. It…
In this document we consider the prime spectrum of an MV-algebra with certain natural operations. These are used to show connections between the classes of prime lattice filters and prime implication filters.
We prove that the lattice of ideals of an arbitrary $L$-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of $L$-algebras and characterize…
We study the PBW-filtration on the highest weight representations $V(\la)$ of the Lie algebras of type ${\tt A}_{n}$ and ${\tt C}_{n}$. This filtration is induced by the standard degree filtration on $\U(\fn^-)$. In previous papers, the…
One of the main open problems in the theory of automorphic products is to classify reflective modular forms. In [Sch06] Scheithauer classified strongly reflective modular forms of singular weight on lattices of prime level. In this paper we…
This paper explores applications of the so-called Freese's technique, a classical approach to study the congruence variety of a given algebra. We leverage this tool to investigate lattices that are admissible as congruence sublattice of a…
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…