For any k ≥ 0, all primes n satisfy the congruence nσk(n) ≡ 2 mod φ(n). We show that this congruence in fact characterizes the primes, in the sense that it is satisfied by only finitely many composite n. This characterization generalizes the results of Lescot and Subbarao for the cases k = 0 and k = 1. For 0 ≤ k ≤ 14, we enumerate the composite n satisfying the congruence. We also prove that an...

Let S be a smooth affine algebraic curve, and let S̊ be the Riemann surface obtained by removing a point from S. We provide evidence for the congruence subgroup property of mapping class groups by showing that the congruence kernel ker ( M̂od(S̊)→ Out ( π̂1(S̊) )) lies in the centralizer of every braid in Mod(S̊). As a corollary, we obtain a new proof of Asada’s theorem that the congruence subgroup p...

Previous research on cross-cultural leadership has examined the effects of leadership-society congruence without explaining how positive outcomes might result when there is a fit between leadership and societal culture, and via which mechanisms the effects of such congruence are transmitted. We fill this gap by developing a culturally contingency model of leader-society value congruence effects...

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics wit...

Let L be a bounded lattice, let [a, b] and [c, d] be intervals of L, and let φ : [a, b] → [c, d] be an isomorphism between these two intervals. Let us consider the algebra L↔ φ = 〈L;∧,∨, φ, φ−1〉, which is a lattice with two partial unary operations. We construct a bounded lattice K (in fact, a convex extension of L) such that the congruence lattice of L↔ φ is isomorphic to the congruence lattic...

Purpose – The purpose of this paper is to describe why trust congruence is important to negotiation, illustrate potential types of trust congruence in negotiating dyads, and link those types of congruence to joint-behavioral outcomes. Design/methodology/approach – Studies pertinent to negotiators’ trust in one another are reviewed, and based on prior theoretical and empirical work, propositions...

We define Euclidean scissor congruence groups for an arbitrary algebraically closed field F and formulate a conjecture describing them. Using the Euclidean and NonEuclidean F–scissor congruence groups we construct a category which is conjecturally equivalent to a subcategory of the category MT (Fε) of mixed Tate motives over the dual numbers Fε := F [ε]/ε . 1. Euclidean scissor congruence group...

Let L be a lattice and let L1, L2 be sublattices of L. Let be a congruence relation of L1. We extend to L by taking the smallest congruence of L containing . Then we restrict to L2, obtaining the congruence L2 of L2. Thus we have de ned a map ConL1 ! ConL2. Obviously, this is an isotone 0-preservingmap of the nite distributive lattice ConL1 into the nite distributive lattice ConL2. The main res...

For e-business, location is irrelevant and competition is intense. To succeed in this environment, organizations must find new ways to differentiate themselves from their competition. One way to achieve e-business differentiation is to foster trust by building a perception of value congruence and avoiding a perception of value conflict. We explore how value congruence contributes to and how val...

Proposition algebra is based on Hoare’s conditional connective, which is a ternary connective comparable to if-then-else and used in the setting of propositional logic. Conditional statements are provided with a simple semantics that is based on evaluation trees and that characterizes so-called free valuation congruence: two conditional statements are free valuation congruent if, and only if, t...