In this paper, we introduce the concept of $\Sigma$-semicommutative ring for $\Sigma$ a finite family of endomorphisms of a ring $R$. We relate this class of rings with other classes of rings such as Abelian, reduced, $\Sigma$-rigid, nil-reversible …
In this paper, we provide a new and more general filtration to the family of noncommutative rings known as skew PBW extensions. We introduce the notion of $\sigma$-filtered skew PBW extension and study some homological properties of these algebras. …
We establish necessary or sufficient conditions to guarantee that skew Poincaré–Birkhoff–Witt extensions are NI or NJ rings. Our results extend those corresponding for skew polynomial rings and establish similar properties for other families of …
In this paper we present a right version of the Buchberger algorithm over skew Poincaré-Birkhoff-Witt extensions (skew PBW extensions for short) defined by Gallego and Lezama [5]. This algorithm is an adaptation of the left case given in [3]. In …
The aim of this paper is to investigate different radicals (Wedderburn radical, lower nil radical, Levitzky radical, upper nil radical, the set of all nilpotent elements, the sum of all nil left ideals) of the noncommutative rings known as skew …
En este artículo, demostramos que el automorfismo de Nakayama de una extensión PBW torcida graduada sobre un álgebra de Koszul finitamente presentada y Auslander-regular tiene determinante homológico trivial. Para A = σ(R)una extensión PBW torcida …
Our purpose in this paper is to characterize skew PBW extensions over several weak symmetric rings. As a consequence of our treatment, we extend results in the literature concerning the property of symmetry for commutative rings and skew polynomial …
En este artículo estudiamos la propiedad χ de álgebras que son extensiones PBW torcidas graduadas. Demostramos que si R = ⊕p≥0Rp es un álgebra noetheriana N-graduada y A = σ(R)⟨x1,...,xn⟩ es una extensión PBW torcida cuasi-conmutativa graduada de R, …
This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated …
In this paper, we introduce weak (Σ,Δ)-compatible rings and study skew Poincaré–Birkhoff–Witt extensions over these rings. We characterize the weak notion of compatibility for several noncommutative rings appearing in noncommutative algebraic …