This paper is a survey of the theory of Chevalley groups over commutative rings, centred
around two topics: explicit calculations in the groups using their minimal modules and the …

This is the first in a series of papers dedicated to the structure of Chevalley groups over
commutative rings. The goal of this series is to systematically develop methods of …

Introduction. Let K be a field. Springer has proved that an anisotropic quadratic form over K
is also anisotropic over any odd degree extension of K (see [31],[14]). If the characteristic of …

An ideal lattice is a pair (I, b), where I is an ideal of a number field, and b is a lattice,
satisfying an invariance relation (see § 1 for the precise definition). Ideal lattices naturally …

This paper studies the work of Bak in algebra and (lower) algebraic K-theory and some later
developments stimulated by them. We present an overview of his work in these areas …

Motivated by the desire for better isomorphism tests for finite groups, we present a
polynomial-time algorithm for deciding isomorphism within a class of p-groups that is well …

Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to
the large and dynamic area of algebras and forms over commutative rings. The book begins …

A theorem is proved on the structure of the group of isometries of a Hermitian map $ b\colon
V\times V\to W $, where $ V $ and $ W $ are vector spaces over a finite field of odd order …

Lorsque L/K est galoisienne de groupe de Galois G, cette forme est invariante par G. On
obtient ainsi ce que l'on appelle une G-forme quadratique, cf. n? 1.2. C'est un invariant de …

Publisher Summary This chapter discusses automorphism groups of positive definite binary
quaternion Hermitian lattices and new mass formula. It presents a general method on the …