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 …

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 …

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 …

In this paper, we study the notion of McCoy ring over the class of non-commutative rings of
polynomial type known as skew Poincaré–Birkhoff–Witt extensions. As a consequence, we …

In this article, we continue the study of ideals of the noncommutative rings of polynomial type
known as skew Poincaré-Birkhoff-Witt extensions. More exactly, we focus on the associated …

In this paper, we investigate the Koszul behavior of finitely semi-graded algebras by the
distributivity of some associated lattice of ideals. The Hilbert series, the Poincaré series, and …

In this paper, we characterize the units of skew PBW extensions over compatible rings. With
this aim, we recall the transfer of the property of being 2-primal for these extensions. As a …

The aim of this article is to develop the theory of skew Armendariz and quasi-Armendariz
modules over skew PBW extensions. We generalize the results of several works in the …

In this paper, we discuss some open problems of non-commutative algebra and non-
commutative algebraic geometry from the approach of skew PBW extensions and semi …

Our aim in this paper is to investigate symmetry and reversibility properties for quantum
algebras and skew PBW extensions. Under certain conditions we prove that these …