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 …
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 …
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 …
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 …
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].
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 …
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 …
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, …
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 …