3 papers
math.RA2025
Graded chain conditions and graded Jacobson radical of groupoid graded modules
Zaqueu Cristiano, Wellington Marques de Souza, Javier Sánchez
In this work, we continue to lay the groundwork for the theory of groupoid graded rings and modules. The main topics we address include graded chain conditions, the graded Jacobson…
math.RA2025
Groupoid Graded Semisimple Rings
Zaqueu Cristiano, Wellington Marques de Souza, Javier Sánchez
We develop the theory of groupoid graded semisimple rings. Our rings are neither unital nor one-sided artinian. Instead, they exhibit a strong version of having local units and bei…
math.RA2025
Algebraic aspects of general free skew extensions of rings
Vitor O. Ferreira, Ãrica Z. Fornaroli, Javier Sánchez
We consider skew free extensions of rings, also known as free multivariate skew polynomial rings, and explore some of the algebraic aspects of this construction. We give different…