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María Camila Ramírez

Publications and source records attributed to María Camila Ramírez.

5 recordsLinked to original sources
arXiv2024

Maps between schematic semi-graded rings

Motivated by Smith's work \cite{Smith2003, Smith2016} on maps between non-commu\-tative projective spaces of the form ${\rm Proj}_{nc} A$ in the setting of non-commutative projective geometry developed by Rosenberg and Van den Bergh, and the notion of schematicness introduced by Van Oystaeyen and Willaert \cite{VanOystaeyenWillaert1995} to $\mathbb{N}$-graded rings with the aim of formulating a non-commutative scheme theory à la Grothendieck \cite{EGAII1961}, in this paper we consider a first approach to maps in the Smith's sense in the more general setting of non-commutative projective spaces over semi-graded rings defined by Lezama and Latorre \cite{LezamaLatorre2017}. We extend Smith's key result \cite[Theorem 3.2]{Smith2003}, \cite[Theorem 1.2]{Smith2016} from the category of schematic $\mathbb{N}$-graded rings to the category of schematic semi-graded rings.

math.AG↗
arXiv2024

A view toward homomorphisms and cv-polynomials between double Ore extensions

Motivated by the theory of homomorphisms and cv-polynomials of Ore extensions formulated by several mathematicians, the rol of double Ore extensions introduced by Zhang and Zhang in the classification of Artin-Schelter regular algebras of dimension four, and that there are no inclusions between the classes of all double Ore extensions of an algebra and of all length two iterated Ore extensions of the same algebra, our aim in this paper is to present a first approach toward a theory of homomorphisms and cv-polynomials between double Ore extensions. We obtain several results on the characterizations of cv-polynomials and their relations with inner derivations of the ring of coefficients of the double algebra, and show that the computation of homomorphisms corresponding to these polynomials is non-trivial. We illustrate our results with different examples including Nakayama automorphisms of trimmed double Ore extensions.

math.RA↗
arXiv2024

On homomorphisms and cv-polynomials between iterated Ore extensions

Motivated by the study of homomorphisms and cv-polynomials presented by Rimmer \cite{Rimmer1978} in the case of Ore extensions of automorphism type, Ferrero and Kishimoto \cite{FerreroKishimoto1980} and Kikumasa \cite{Kikumasa1990} in the setting of these extensions of derivation type, and Lam and Leroy \cite{LamLeroy1992} in the context of Ore extensions of mixed type over division rings, in this paper we investigate these both notions for iterations of these extensions. We show that the iteration of some of the results presented in those papers is non-trivial, and illustrate our treatment with several noncommutative algebras.

math.RA↗