We use methods of the general theory of congruence and *congruence for complex matrices—regularization and cosquares—to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that ĀA (respectively, A) is normal. As special cases of our canonical forms, we obtain—in a coherent and systematic way—known canonical forms for con...

We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...

We prove that if V is a variety of algebras (i.e., an equationally axiomatizable class of algebraic structures) in a finite language, V has a difference term, and V has a finite residual bound, then V is finitely axiomatizable. This provides a common generalization of R. McKenzie’s finite basis theorem for congruence modular varieties with a finite residual bound, and R. Willard’s finite basis ...

The Cauchy-Davenport theorem states that if A and B are nonempty sets of congruence classes modulo a prime p, and if |A| = k and |B| = l, then the sumset A + B contains at least min(p, k + l − 1) congruence classes. It follows that the sumset 2A contains at least min(p, 2k − 1) congruence classes. Erdős and Heilbronn conjectured 30 years ago that there are at least min(p, 2k − 3) congruence cla...

In this paper we construct a pullback formula of a Siegel Eisenstein series on GU(3, 3) to GSp(4) × GL(2) and use it to study the Bloch-Kato conjecture for automorphic forms on GL(2). Let f ∈ S2k−2(SL2(Z)) be a normalized eigenform and let p > 2k− 2 be a prime so that p | Lalg(k, f). Then up to some reasonable hypotheses, we use this formula to construct a congruence between the Saito-Kurokawa ...

According to the so-called “mirroring hypothesis”, the structure of an organization tends to replicate the technical dependencies among the different components in the product (or service) that the organization is developing. An explanation for this phenomenon is that socio-technical alignment, which can be measured by the congruence of technical dependencies and human relations (Cataldo et al....

Congruence is the degree to which one’s personality matches one’s behavior in a particular situation. On four separate occasions over several weeks, 202 undergraduate participants described a situation they encountered the previous day and their behavior. Analyses considered overall congruence as well as distinctive congruence, adjusted for the match of personality and behavior to the normative...

Over the past two decades, research and popular discourse have taken up the question of whether strong racial group identification inhibits or promotes achievement motivation among African American students. However, scant attention has been paid to contextual variation in roles and functions of racial identity. In this chapter, we considered how the congruence between students’ racial identity...

Several studies have investigated the age-related impact in cognitive action control. However, to our knowledge, none of the studies have focused on the effect of moderate age on the strength of automatic activation according to the activation-suppression model. We therefore investigated the effect of moderate age on cognitive action control using an oculomotor version of the Simon task and dis...