# Uniform Dimension over Skew PBW Extensions

@inproceedings{Reyes2014UniformDO, title={Uniform Dimension over Skew PBW Extensions}, author={Armando Reyes}, year={2014} }

The aim of the present paper is to show that, under some conditions, the uniform dimension of a ring R is the same as the uniform dimension of a skew Poincare-Birkhoff-Witt extension built on R.

## 19 Citations

PBW bases for some 3-dimensional skew polynomial algebras

- Mathematics
- 2017

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.

Minimal prime ideals of skew PBW extensions over 2-primal compatible rings

- Mathematics
- 2020

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 consequence…

On the ACCP in skew Poincaré–Birkhoff–Witt extensions

- Mathematics
- 2018

The objective of this paper is to investigate the ascending chain condition on principal left (resp. right) ideals of noncommutative rings known as skew PBW extensions. We consider these extensions…

Enveloping Algebra and Skew Calabi-Yau algebras over Skew Poincar\'e-Birkhoff-Witt Extensions

- Mathematics
- 2017

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…

$\sigma$-PBW Extensions of Skew Armendariz Rings

- Mathematics
- 2016

The aim of this paper is to investigate a general notion of $\sigma$-PBW extensions over Armendariz rings. As an application, the properties of being Baer, quasi-Baer, p.p. and p.q.-Baer are…

A notion of compatibility for Armendariz and Baer properties over skew PBW extensions

- Mathematics
- 2017

In this paper we are interested in studying the properties of Armendariz, Baer, quasi-Baer, p.p. and p.q.-Baer over skew PBW extensions. Using a notion of compatibility, we generalize several…

Armendariz modules over skew PBW extensions

- MathematicsCommunications in Algebra
- 2019

Abstract 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 literature…

A generalized Koszul property for skew PBW extensions

- Mathematics
- 2017

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…

Koszulity for skew PBW extensions over fields

- Mathematics
- 2016

Koszul and homogeneous Koszul algebras were defined by Priddy in \cite{Priddy1970}. There exist some relations between these algebras and the skew PBW extensions introduced in \cite{LezamaGallego}.…

Q A ] 2 0 D ec 2 01 6 Armendariz Modules over Skew PBW Extensions

- 2018

The aim of this paper 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 literature concerning Ore…

## References

SHOWING 1-10 OF 22 REFERENCES

Goldie rank of ore extensions

- Mathematics
- 1995

This paper is concerned with the problem when an Ore extension R[t, S, D] has the same Goldie rank as the coefficient ring R. It is shown, in particular, that this is the case when either R is…

Goldie Conditions for Ore Extensions over Semiprime Rings

- Mathematics
- 2004

Abstract
Let R be a ring, σ an injective endomorphism of R and δ a σ-derivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ,δ] and both rings…

Gröbner Bases for Ideals of σ-PBW Extensions

- Mathematics
- 2010

In this article, we introduce the σ-PWB extensions and construct the theory of Gröbner bases for the left ideals of them. We prove the Hilbert's basis theorem and the division algorithm for this more…

Gelfand-Kirillov Dimension of Skew PBW Extensions

- Mathematics
- 2013

Gelfand-Kirillov dimension of Poincar e-Birkho-Witt ( PBW for short) extensions was established by Matczuk ((15), Theorem A). Since PBW extensions are a particular example of skew PBW extensions…

Some Homological Properties of Skew PBW Extensions

- Mathematics
- 2013

We prove that if R is a left Noetherian and left regular ring then the same is true for any bijective skew PBW extension A of R. From this we get Serre's Theorem for such extensions. We show that…

Embeddings of differential operator rings and Goldie dimension

- Mathematics
- 1988

The differential operator ring S = R[x; 6} can be embedded in Ai(R), the first Weyl algebra over R, where R is a Q-algebra and S is a locally nilpotent derivation on R. Furthermore Ai(R) is again a…

Krull dimension of differential operator rings. III. Noncommutative coefficients

- Mathematics
- 1983

This paper is concerned with the Krull dimension (in the sense of Gabriel and Rentschler) of a differential operator ring S[9; 8], where S is a right noetherian ring with finite Krull dimension n and…

Lectures on modules and rings

- Mathematics
- 1998

1 Free Modules, Projective, and Injective Modules.- 1. Free Modules.- 1A. Invariant Basis Number (IBN).- 1B. Stable Finiteness.- 1C. The Rank Condition.- 1D. The Strong Rank Condition.- 1E.…

Noncommutative Noetherian Rings

- Mathematics
- 2001

Articles on the history of mathematics can be written from many dierent perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop…