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Armando Reyes

Publications and source records attributed to Armando Reyes.

At least 19 recordsLinked to original sources
arXiv2026

On the category of semi-graded modules

Lezama \cite{LezamaLatorre2017} introduced the notion of semi-graded ring with the aim of generalizing $\mathbb{Z}$-graded rings and several families of noncommutative rings of polynomial type non-$\mathbb{N}$-graded such as the skew Poincaré-Birkhoff-Witt extensions defined by him \cite{GallegoLezama2010}. In a series of papers, \cite{Lezama2020, Lezama2021, LezamaGomez2019, LezamaLatorre2017}, he studied problems of non-commutative projective algebraic geometry generalizing the original ideas of Artin et al. \cite{Artin1992, ArtinSchelter1987, ArtinTateVandenBergh2007, ArtinTateVandenBergh1991, ArtinZhang1994} on $\mathbb{N}$-graded rings, in the categorical context of the category $\mathsf{SGR}-R$ of left semi-graded modules over a semi-graded ring $R$. In this note we prove that $\mathsf{SGR}-R$ possesses a canonical set of free generators via shifted twists, which endows the category with a {\em Grothendieck structure} and guarantees the existence of enough injective and projective objects. This categorical robustness allows us to formulate a semi-graded analogue of Baer's criterion for injectivity and to establish a first approach to the dual theory of projective resolutions using shifted twists.

math.CT↗
arXiv2026

Combinatorial aspects of normal ordering of 3-dimensional skew polynomial rings

In this paper, we discuss combinatorial aspects of normal ordering of 3-dimensional skew polynomial rings defined and classified by Bell and Smith \cite{BellSmith1990}. With some help of the Mathematical software \texttt{SageMath}, we are able to reduce the length of computation of PBW forms and normal orderings appearing in commutation rules of these algebras.

math.CO↗
arXiv2026

On the smoothness of 3-dimensional skew polynomial rings

This paper is part of a series of papers in which we have investigated the differential smoothness of families of noncommutative algebras. Here, we consider this topic for the family 3-dimensional skew polynomial rings characterized by Bell and Smith \cite{BellSmith1990}.

math.DG↗
arXiv2025

Nilpotent graphs over skew PBW extensions

We investigate the diameter and girth of the nilpotent graph for skew PBW extensions over $2$-primal rings, generalizing similar results on skew polynomial rings. Under certain compatibility conditions, we establish bounds for the diameter of the nilpotent graph and prove invariance of the girth under polynomial extensions.

math.RA↗
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↗