graduation at Matemática from Universidade Estadual de Campinas (2024). (Source: Lattes Curriculum)
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In this master's project we shall study classical topics in the theory of algebras with polynomial identities, namely the identities satisfied by matrix algebras. We shall begin with a brief introduction to the area: polynomial identities, PI algebras, varieties of algebras, T-ideals, the linearization process, homogeneous and multilinear structure of relatively free algebras, the theory …
In this research project we shall study the structure of rings and algebras, towards some applications. We shall start with the basic properties of the rings such as primitiveness, semi-simplicity, the Jacobson radical, the Chain conditions, then we shall go to simple rings, and the Wedderburn--Artin theorem. We shall go into details about simple algebras and the Skolem--Noether theorem, …
The main objective of this project is to provide a strong mathematical foundation to the student, through the development of measure theory and principles of ergodic theory, such as the main properties related to mixing properties, transfer operators and some applications of ergodic theory to algebraic systems.
| 1 / 1 | Ongoing scholarships in Brazil |
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