Some topics on groupoid graded rings

• Grant number: 22/11166-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: December 01, 2022
• End date: August 06, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Javier Sanchez Serda
• Grantee: Caio Antony Gomes de Matos Andrade
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 20/16594-0 - Non commutative rings and applications, AP.TEM
• Associated scholarship(s): 23/11994-9 - Groupoid graded rings and groupoid rings: their categories of modules and units, BE.EP.DR

Abstract

This project for a Ph.D. thesis focuses on groupoid graded rings with two main topics. On the one hand, we will study the existence of graded homomorphisms from a groupoid graded ring to groupoid graded division rings, i.e. we intend to extend Cohn's theory to this setting as well as the result of Malcomsom and Schofield on homomorphisms of rings to division rings. On the other hand, we will study the connection between several rings and categories associated to groupoid graded rings.