This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

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 [1] and [2] DD Anderson and DF Anderson studied commutative. integral domains that are
graded by a torsion-free abelian group and that satisfy a certain arithmetical property (such …

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 …

LetRbe a Dedekind domain with quotient fieldKand letGbe a finite group. Let α: G× G→ R\{0}
be a generalized 2-cocycle, ie, not necessarily taking its values in the units ofR, and …

In [14], Van Oystaeyen introduced the so-called graded Brauer group Brg (R) of a P-graded
commutative ring, in order to study the Brauer group of a projective variety (cf.[16]). The …

One of the fundamental questions in the study of Grothendieck groups of commutative rings
is the following: does stable isomorphism of two modules entail that they are isomorphic …

In 1971, M. Artin proved the following fundamental result: if S is an etale extension of a
Noetherian commutative ring R, and T is an etale covering of S 0 S, then there exists an …