The term The Theory of Rings seems first used as title of a book by Jacobson [43], and in his
preface Jacobson asserts that the theory that forms the subject of the book had its beginning …

The algebraic theory of quadratic forms originates from the well-known paper [W] of Witt
(1937), where he introduced for the first time the so called Witt ring of a field, ie the ring of all …

We prove several results on reductive group schemes over LG-rings, eg, existence of
maximal tori and conjugacy of parabolic subgroups. These were proven in SGA3 for the …

We provide a detailed study of torsors over Laurent polynomial rings under the action of an
algebraic group. As applications we obtained variations of Raghunathan's results on torsors …

The main thrust of this work is the study of two seemingly unrelated questions: Non-abelian
Galois cohomology of Laurent polynomial rings on the one hand, while on the other, a class …

Let A be a C*-algebra with identity, and let Aut A be the group of all*-automorphisms of A
endowed with the norm topology. In their systematic investigation [22] of Aut A, Kadison and …

We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S
as defined by Calm {\e} s and Fasel, generalizing the case of quadratic pairs on central …

Let R be a commutative ring with identity. In this paper we propose an extension of the
concept of central separable R-algebra and use this to define an associated Brauer group …

We investigate a notion of Azumaya algebras in the context of structured ring spectra and
give a definition of Brauer groups. We investigate their Galois theoretic properties, and …

Let A and B be rings and Mand Në a right A-module and a right B-module respectively. Let
a: End (MA)→ End (NB) be either an isomorphism or an anti-isomorphism of their …