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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.

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