相关论文: What is the weakest idempotent Maltsev condition t…

In this paper we show an explicit relation between chains of torsion classes and weak stability conditions over an abelian category. In particular, up to a natural equivalence, they coincide. We investigate topological properties of the…

The main result of this paper shows that if $\mathcal{M}$ is a consistent strong linear Maltsev condition which does not imply the existence of a cube term, then for any finite algebra $\mathbb{A}$ there exists a new finite algebra…

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…

We establish a direct correspondence between two congruence poroperties for finite algebras. The first property is that minimal sets of type i omit tails. The second property is that congruence lattices omit pentagons of type i.

Let $G$ be a locally compact amenable group. We say that G has property (M) if every closed subgroup of finite covolume in G is cocompact. A classical theorem of Mostow ensures that connected solvable Lie groups have property (M). We prove…

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…

In this paper, we characterize the congruences of an arbitrary i--lattice, investigate the structure of the lattice they form and how it relates to the structure of the lattice of lattice congruences, then, for an arbitrary non--zero…

The notion of a weakly Mal'tsev category, as it was introduced in 2008 by the third author, is a generalization of the classical notion of a Mal'tsev category. It is well-known that a variety of universal algebras is a Mal'tsev category if…

We consider connections between similar sublattices and coincidence site lattices (CSLs), and more generally between similar submodules and coincidence site modules of general (free) $\mathbb{Z}$-modules in $\mathbb{R}^d$. In particular, we…

Approximate lattices are aperiodic generalisations of lattices of locally compact groups that were first studied in seminal work of Yves Meyer. They are defined as those uniformly discrete approximate subgroups (symmetric subsets stable…

Gopal Prasad and A. S. Rapinchuk defined a notion of weakly commensurable lattices in a semisimple group, and gave a classification of weakly commensurable Zariski dense subgroups. A motivation was to classify pairs of locally symmetric…

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…

A compact symplectic manifold $(M, \omega)$ is said to satisfy the hard-Lefschetz condition if it is possible to develop an analogue of Hodge theory for $(M, \omega)$. This loosely means that there is a notion of harmonicity of differential…

Relationship is clarified between the notions of linear extension of algebraic theories, and central extension, in the sense of commutator calculus, of their models. Varieties of algebras turn out to be nilpotent Maltsev precisely when…

We initiate in this article the study of weakly exact structures, a generalization of Quillen exact structures. We introduce weak counterparts of one-sided exact structures and show that a left and a right weakly exact structure generate a…

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…

Let $L$ be a finite lattice and let $I$ be an ideal of $L$. Then the restriction map is a bounded lattice homomorphism of the congruence lattice of~$L$ into the congruence lattice of $I$. In a 2009 paper, the authors proved the converse. In…

In a recent letter [Information Processing Letters~104 (2007) 152-158], it has shown some sufficient conditions for commutativity of quantum weakest preconditions. This paper provides some alternative and simple characterizations for the…

Let $S$ be an additively idempotent semiring and $\mathbf{M}_n(S)$ be the semiring of all $n\times n$ matrices over $S$. We characterize the conditions of when the semiring $\mathbf{M}_n(S)$ is congruence-simple provided that the semiring…

We study the existence of nontrivial and of representable (dual) weak complementations, along with the lattice congruences that preserve them, in different constructions of bounded lattices, then use this study to determine the finite…