Algebra Introduction - An Approach via Module Theory

• Grant number: 25/04211-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Claudemir Fideles Bezerra Júnior
• Grantee: Mateus José da Silva Costa
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/04011-9 - Struture of graded and/or trace algebras, and Invariant theory, AP.R

Abstract

The mastery of concepts in Abstract Algebra is fundamental for the development of research in modern mathematics. In this sense, the goal of this Scientific Initiation project is to study the representation theory of a group G over a field K as a KG-module, in order to better understand the behavior of these mathematical objects. To achieve this, it will be necessary to consolidate a theoretical foundation in group theory, rings, and modules, which will provide the student with a solid introduction to Algebra. As the main bibliography, we will adopt the book Algebra - An Approach via Module Theory by William A. Adkins and Steven H. Weintraub. This text covers all the necessary content for the development of the project and includes an extensive collection of exercises, offering a wide range of opportunities for Mateus to develop his skills in the field.