Noncommutative Algebra

𝜎-PBW Extensions of Skew Armendariz Rings

The aim of this paper is to investigate a general notion of 𝜎-PBW extensions over Armendariz rings. As an application, the properties of Baer, quasi-Baer, p.p., and p.q.-Baer are established for these extensions. We generalize several results in the …

Enveloping algebra and Calabi-Yau algebras over skew Poincaré-Birkhoff-Witt extensions

In this paper, we show that the tensor product of skew PBW extensions is a skew PBW extension. We also characterize the enveloping algebra of a skew PBW extension. Finally, we establish conditions for sufficiency to guarantee the property of being …

Koszulity for graded skew PBW extensions

Pre-Koszul and Koszul algebras were defined by Priddy [15]. There exist some relations between these algebras and the skew PBW extensions defined in [8]. In [24] we gave conditions to guarantee that skew PBW extensions over fields it turns out …

Koszulity for skew PBW extensions over fields

Koszul and homogeneous Koszul algebras were defined by Priddy in [18]. There exist some relations between these algebras and the skew PBW extensions introduced in [7]. In this paper, we give conditions to guarantee that skew PBW extensions over …

PBW bases for some 3-dimensional skew polynomial algebras

The aim of this paper is to establish necessary and sufficient algorithmic conditions to guarantee that an algebra is actually a 3-dimensional skew polynomial algebra in the sense of Bell and Smith [1].

Bases for quantum algebras and skew Poincaré-Beirkhoff-Witt extensions

Considering quantum algebras and skew Poincaré-Birkhoff-Witt (PBW for short) extensions defined by a ring and a set of variables with relations between them, we are interesting in finding a criteria and some algorithms which allow us to decide …

Calabi-Yau property for graded skew PBW extensions

Graded skew PBW extensions were defined by the first author as a generalization of graded iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter regularity and the (skew) Calabi- Yau condition for this kind of …

A note on Zip and reversible skew PBW extensions

In this note we establish necessary and sufficient conditions to guarantee the existence of zip and reversible skew PBW extensions.

Armendariz property for skew PBW extensions and their classical ring of quotients

Consideramos un primer acercamiento a la noción de anillo de Armendariz para una extensión torcida de Poincaré-Birkho-Witt (PBW), y su anillo clásico de cocientes. Como una aplicación inmediata de este tratamiento, estudiamos las propiedades de Baer, …

Some remarks about the cyclic homology of skew PBW extensions

We study the cyclic homology for a class of noncommutative polynomial rings known as skew PBW extensions. We obtain explicit computations for some important families of such extensions over fields. In particular, we consider the cyclic homology of …