Related papers: Armendariz Modules over Skew PBW Extensions
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 that Abelian, reduced, $\Sigma$-rigid,…
In this paper we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew PBW extensions. Moreover, we find a counterexample to the conjecture proposed in…
We examine PBW deformations of finite group extensions of skew polynomial rings, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of…
In this paper we review some classical results on the algebraic dependence of commuting elements in several noncommutative algebras as differential operator rings and Ore extensions. Then we extend all these results to a more general…
In this paper, we study the reflexive-nilpotents-property (briefly, RNP) for Ore extensions of injective type, and more generally, skew PBW extensions. With this aim, we introduce the notions of $\Sigma$-skew CN rings and $\Sigma$-skew…
A ring $R$ is said to be an almost Armendariz ring if whenever product of two polynomials in $R[x]$ is zero, then product of their coefficients are in $N_{*}(R)$. In this article, for an endomorphism $\alpha$ on $R$, we define an…
In this paper, we study the uniform dimension and the associated prime ideals of induced modules over skew PBW extensions.
In this paper we show that the tensor product of skew PBW extensions is a skew PBW ex- tension. We also characterize the enveloping algebra of a skew PBW extension. Finally, we establish sufficient conditions to guarantee the property of…
Graded quasi-commutative skew PBW extensions are isomorphic to graded iterated Ore extensions of endomorphism type, whence graded quasi-commutative skew PBW extensions with coefficients in AS-regular algebras are skew Calabi-Yau and the…
In this paper we investigate extended modules for a special class of Ore extensions. We will assume that $R$ is a ring and $A$ will denote the Ore extension $A:=R[x_1,\dots,x_n;\sigma]$ for which $\sigma$ is an automorphism of $R$,…
In [1] the author gives a description of Poisson brackets on some algebras of quantum polynomials $\mathcal{O}_q$, which is called\textit{ general algebra of quantum polynomials}. The main of this paper is to present a generalization of [1]…
Birkenmeier and Heider, in [2], say that a ring R is right cP-Baer if the right annihilator of a cyclic projective right R-module in R is generated by an idempotent. These rings are a generalization of the right p.q.-Baer and abelian rings.…
Let R be a commutative algebra. In this paper we show that constant skew PBW extensions of a generalized Koszul algebra R are also generalized Koszul. Let A be a semi-commutative skew PBW extension of R such that A is R-augmented. We show…
In this work, we set up a theory of p-adic modular forms over Shimura curves over totally real fields which allows us to consider also non-integral weights. In particular, we define an analogue of the sheaves of k-th invariant differentials…
We give the basic structure of the multivariable Ore extensions $S=A[\underline{t} ; \sigma, \underline{\delta}]$ introduced in the work of Mart\'inez-Pe\~nas and Kschischang. The Pseudo multilinear transformations (PMT's) are introduced…
In this paper we describe the prime ideals of some important classes of skew PBW extensions, using the classical technique of extending and contracting ideals. Skew PBW extensions include as particular examples Weyl algebras, enveloping…
In this paper we introduce the semi-graded rings, which extend graded rings and skew PBW extensions. For this new type of non-commutative rings we will discuss some basic problems of non-commutative algebraic geometry. In particular, we…
We investigate the differential smoothness of a certain family of skew Poincar\'e-Birkhoff-Witt extensions.
We investigate and characterize several kinds of elements such as units, idempotents, von Neumann regular, $\pi$-regular and clean elements for skew PBW extensions over weak compatible rings. We also study the notions of Gelfand and…
For sigma-PWB extensions, we extend to modules the theory of Gr\"obner bases of left ideals presented in [5]. As an application, if A is a bijective quasi-commutative sigma-PWB extension, we compute the module of syzygies of a submodule of…