Graded rings of quotientes of groupoid graded rings

• Grant number: 21/14132-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2022
• End date: February 29, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Javier Sanchez Serda
• Grantee: Zaqueu Cristiano Moreira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In Algebra, it is useful to embed a ring in a new one with better properties. An important example of this is the technique of localization at (the complement of) a prime ideal. In non-commutative algebra it is not always possible the construction of a ring of fractions. Ore localization provides necessary and sufficient conditions in a ring for the existence o a localization similar to the commutative one. There also exist results that explain when this new localized ring is a division ring, a simple artinian ring, etc.The general theory of rings of quotients arose in order to construct rings "of quotients" for a greater class of rings. For example, the maximal ring of quotients exists for any ring. Depending on the properties we expect our quotient ring to have, we will use one or another sort of ring of quotients.Given a ring R graded by a grupoid “, it is natural to ask if there exists an embedding of R in another “-graded ring with better properties than R. In this project, we would like to develop the theory of “-graded rings of quotients of rings graded by a grupoid. Particularly, we will concentrate on the construction of the maximal graded ring of quotients, of the graded Martindale ring of quotients and of the symmetric graded Martindale ring of quotients.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MOREIRA, Zaqueu Cristiano. Graded rings of quotients of groupoid graded rings. 2024. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.