Cancellative semigroup rings which are Azumaya algebras

Umbral Calculus and Cancellative Semigroup Algebras∗

We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of cancellative semigroup, their convolution algebras, and tokens between them provides a common language for description of objects from these three fields.

An algorithm for commutative semigroup algebras which are principal ideal rings

Associative and commutative algebras with identity have various well-known applications. In particular, many classical codes are ideals in commutative algebras (see [4], [12] for references). Computer storage, encoding and decoding algorithms simplify if all these codes have single generator polynomials. Thus it is of interest to determine when all ideals of an algebra are principal. In [5] Dec...

There Are Enough Azumaya Algebras on Surfaces

Using Maruyama’s theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles on proper normal algebraic surfaces.

Azumaya algebras and derivations

Motives of Azumaya Algebras

We study the slice filtration for the K-theory of a sheaf of Azumaya algebras A, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson-Lichtenbaum conjecture, we apply our results to show the vanishing of SK2(A) for a central simple algebra A of square-free index (prime to the characteristic). This pro...