Structure theory of graded central simple algebras

This work is focused on the structure theory of graded central simple algebras. We consider algebras graded by Z/pqZ where p and q are distinct primes different than 2. I define a new algebra type, called a p-odd algebra, and a structure theorem for these algebras. This definition and structure theorem are a generalization of the current results in the literature. We define and discuss the graded Brauer group in this context and its relation to the structure of the algebras. Moreover, we define a group of invariants and show how to view the classical Brauer group as a subgroup of the graded Brauer group.