Groupoid graded rings and groupoid rings: their categories of modules and units
Galois Theory, profinite groups and applications in quadratic forms
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Graded rings of quotients of groupoid graded rings
Full text
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| Author(s): |
Zaqueu Cristiano Moreira
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2024-02-21 |
| Examining board members: |
Vitor de Oliveira Ferreira;
Dolors Herbera;
Mercedes Siles Molina
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| Advisor: | Javier Sanchez Serdà |
| Abstract | |
In this work, we study the graded maximal and the graded Martindale right (left, symmetric) rings of quotients of groupoid graded rings. In order to define and prove properties of these graded rings of quotients, we generalized several concepts and results from Ring Theory and Group Graded Ring Theory to the groupoid graded context, some of which did not exist in the literature yet. We characterize when the graded maximal right ring of quotients is a von Neumann gr-regular ring and when it is a gr-semisimple ring. Motivated by the example of small preadditive categories, we defined what would be the maximal and the Martindale right (left, symmetric) category of quotients of a preadditive category. (AU) | |
| FAPESP's process: | 21/14132-2 - Graded rings of quotientes of groupoid graded rings |
| Grantee: | Zaqueu Cristiano Moreira |
| Support Opportunities: | Scholarships in Brazil - Master |