In the study of the Brauer group, Br (D), of a commutative ring D, the subgroup Br (S/D),
consisting of the classes a E Br (D) split by the ringextension S of D, play, a fundamental …

Topic of this paper is the study of certain relations between the Brauer group of a Z-graded
commutative ring C and a so called" graded" Brauer group (par abus de language) obtained …

In this paper we aim to present a~~ homological interperation of the graded Brauer group of
a Z-graded comtative ring R, as introduced in [I31 by F. Van Oystaeyen. This graded Brauer …

O. Introduction. If C is a commutative graded ring, then it seems to be a natural question to
ask in what way the presence of the graded structure on the ring reflects in the structure of …

It is a well-known fact in the theory of Brauer groups of commutative rings, that there exists a
natural monomorphism Br (R)~ H2 (R, U), where H2 (R, U) is the~ tale Brauer group of R. As …

Generalized crossed products, sometimes called strongly graded rings, appear quite
naturally in the theory of splitting rings for Azumaya algebras over rings with nontrivial Picard …

Let $ G $ be a finite abelian group, and $ R $ a commutative ring. The Brauer-Long group
$\operatorname {BD}(R, G) $ is described by an exact sequence\[1\to {\operatorname {BD} …

Let R be a commutative ring and G a finite abelian group. In [8], Long developed a Brauer
group theory for G-dimodule algebras (ie, algebras with a compatible G-grading and G …

This book introduces various notions defined in graded terms extending the notions most
frequently used as basic ingredients in the theory of Azumaya algebras: separability and …

In this paper we develop a Brauer group theory for algebras which are group graded and
acted upon by the same group. This generalizes some recent work of Knus and Childs …