An introduction to abstract algebra and division algebras

• Grant number: 23/10439-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2023
• End date: September 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Dimas José Gonçalves
• Grantee: Pedro Augusto Bussola
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this project, the student will study, in an introductory way, the theories of groups, rings, fields and finite dimensional division algebras. In particular, the theorems of Frobenius and Wedderburn will be seen, which concern the classification of finite dimensional real division algebras and the commutativity of finite division rings, respectively.