相关论文: Dedekind's Transposition Principle for lattices of…

We review principal results on axiomatizability of classes of lattices of equivalences

In this paper we define Diophantine exponents of lattices and investigate some of their properties. We prove transference inequalities and construct some examples with the help of Schmidt's subspace theorem.

The main results of the paper points out the connection between the weak ordered relations and factor lattices defined by tolerances. It is proved that for any tolerance $T$ of a lattice $L$ the Dedekind-Mac Neille completion of $L/T$ is…

In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.

One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…

In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.

We prove that an analogue of Rogers' theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings…

The apparent discrepancy between the bending of light predicted by the equivalence principle and its corresponding value in general relativity is resolved by evaluating the deflection of light with respect to a direction that is parallel…

We develop a Van der Waerden type theorem in an axiomatic setting of graded lattices and show that this axiomatic formulation can be applied to various lattices, for instance the set partition and the Boolean lattices. We derive the…

Congruence lattices of semiprime algebras from semi--degenerate congruence--modular varieties fulfill the equivalences from B. A. Davey`s well--known characterization theorem for $m$--Stone bounded distributive lattices, moreover, changing…

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.

We consider a class of homogeneous self-similar sets with complete overlaps and give a sufficient condition for the Lipschitz equivalence between members in this class.

We apply a categorical lens to the study of betweenness relations by capturing them within a topological category, fibred in lattices, and study several subcategories of it. In particular, we show that its full subcategory of finite objects…

In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…

We prove a uniform version of the Goldblatt-Thomason theorem for logics algebraically captured by normal lattice expansions (normal LE-logics).

We prove a power series ring analogue of the Dedekind-Mertens lemma. Along the way, we give limiting counterexamples, we note an application to integrality, and we correct an error in the literature.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

We prove a polynomially effective equidistribution result for expanding translates in the space of $d$-dimensional affine lattices for any $d\ge 2$.

We prove a version of adelic descent for continuous localizing invariants.

In this work we investigate the transfer of fundamental order and completeness properties between truncated Riesz spaces and their unitizations. Specifically, we provide characterizations and equivalences for several notions of…