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...

In 1994, the well-known Diie-Hellman key exchange protocol was for the rst time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number eld. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function e...

We show that the poset of regions (with respect to a canonical base region) of a supersolvable hyperplane arrangement is a congruence normal lattice. Specifically, the poset of regions of a supersolvable arrangement of rank k is obtained via a sequence of doublings from the poset of regions of a supersolvable arrangement of rank k − 1. An explicit description of the doublings leads to a proof t...

Every quasigroup (loop, Bol loop, group, respectively) is isomorphic to the factor of a subdirectly irreducible quasigroup (loop, Bol loop, group, respectively) over its monolithic congruence.

BACKGROUND Medical records that do not accurately reflect the patient's current medication list are an open invitation to errors and may compromise patient safety. METHODS This cross-sectional study compares primary care provider (PCP) medication lists and pharmacy claims for 100 patients seen in 8 primary care practices and examines the association of congruence with demographic, clinical, a...

We prove the transfer congruence between p-adic Hecke L-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer’s congruence. The ingredients of the proof include the comparison between Hilbert modular varieties, the q-expansion principle, and some modification of Hsieh’s Whittaker model for Katz’ Eisenstein series. As a first application, we prov...