In this article, we present necessary and sufficient conditions for a graded (trimmed) double Ore extension to be a graded (quasi-commutative) skew PBW extension. Using this fact, we prove that a graded skew PBW extension A=σ(R)⟨x1,x2⟩ of an …
In this paper we present a computational package developed for making computations involved in many homological applications of the Gr"obner theory of skew PBW extensions.
In this paper we study skew Poincaré–Birkhoff–Witt extensions over weak zip rings. Since these extensions generalize Ore extensions of injective type and another noncommutative rings of polynomial type, we unify and extend several results in the …
Let R be an Artin-Schelter regular algebra and A = σ(R)⟨x1,...,xn⟩ a graded quasi-commutative skew PBW extension over R. In this paper we describe the Nakayama automorphism of A using the Nakayama automor- phism of the ring of coefficients R. We …
En este artículo se relacionan algunas estructuras de álgebra de Hopf sobre extensiones de Ore y extensiones PBW torcidas de un álgebra de Hopf. Estas relaciones son ilustradas con ejemplos. También se demuestra que las extensiones Hopf Ore y las …
In this short note we present an elementary matrix-constructive algorithmic proof of the Quillen-Suslin theorem for Ore extensions $A:=K[x;\sigma, \delta]$, where $K$ is a division ring, $\sigma: K \to K$ is a division ring automorphism and $\sigma: …
In this paper, we study extended modules for a special class of Ore extensions. We will assume that $R$ is a ring and $A$ will denote the Ore extension $A:=R[x_1, \ldots, x_n:\sigma]$ for which $\sigma$ is an automorphism of $R$, $x_ix_j = x_jx_i$ …
Reviewing some classical results on the algebraic dependence of commuting elements in several noncommutative algebras as differential operator rings and Ore extensions, we extend these results in a more general setting of the family of noncommutative …
In this paper we are interested in studying the properties of Armendariz, Baer, quasi-Baer, p.p. and p.q.-Baer over skew PBW extensions. Using a notion of compatibility, we generalize several propositions established for Ore extensions and present …
The objective of this paper is to investigate the ascending chain condition on principal left (resp. right) ideals of noncommutative rings known as skew PBW extensions. We consider these extensions over domains and over Sigma-rigid rings. We unify …