Grassmann algebra, graded algebras, PI-equivalence
Let E be the infinite dimensional Grassmann algebra and Z be the infinite cyclic group. In the development of Kemer's Theory, algebra E plays a crucial role. It is important to mention that such algebra occurs in various contexts, such as Analysis, Geometry, in addition to PI-theory itself.
In recent years, abelian gradings on E and the respective graded identities have been addressed in several research articles, and it is still a very fertile topic at the research level. Therefore, the focus of our dissertation is to study recent results on gradings on E by the group Z. We will study results on the construction of graduations in E, graded identities, conditions for PI-equivalence and non-isomorphism, etc. We also intend to underline the correlation between this theme and Elementary Number Theory techniques.