scholarly journals Uniform Dimension over Skew PBW Extensions

2014 ◽  
Vol 48 (1) ◽  
pp. 79-96 ◽  
Author(s):  
Armando Reyes
Keyword(s):  
Uniform Dimension ◽  
Skew Pbw Extensions

On commutative rings with uniserial dimension

2014 ◽  
Vol 14 (01) ◽  
pp. 1550008 ◽  
Author(s):  
A. Ghorbani ◽  
Z. Nazemian
Keyword(s):  
Commutative Ring ◽  
Commutative Rings ◽  
Artinian Rings ◽  
Uniform Dimension ◽  
Uniserial Modules

In this paper, we define and study a valuation dimension for commutative rings. The valuation dimension is a measure of how far a commutative ring deviates from being valuation. It is shown that a ring R with valuation dimension has finite uniform dimension. We prove that a ring R is Noetherian (respectively, Artinian) if and only if the ring R × R has (respectively, finite) valuation dimension if and only if R has (respectively, finite) valuation dimension and all cyclic uniserial modules are Noetherian (respectively, Artinian). We show that the class of all rings of finite valuation dimension strictly lies between the class of Artinian rings and the class of semi-perfect rings.

scholarly journals Hopf algebras and skew PBW extensions

2019 ◽  
Vol 10 (2) ◽  
Author(s):  
Luis Alfonso Salcedo Plazas
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Ore Extensions ◽  
Skew Pbw Extensions

In this article we relate some Hopf algebra structures over Ore extensions and over skew PBW extensions ofa Hopf algebra. These relations are illustrated with examples. We also show that Hopf Ore extensions andgeneralized Hopf Ore extensions are Hopf skew PBW extensions.

scholarly journals Uniform Dimension Results for the Brownian Sheet

1989 ◽  
Vol 17 (4) ◽  
pp. 1454-1462 ◽  
Author(s):  
T. S. Mountford
Keyword(s):  
Brownian Sheet ◽  
Uniform Dimension

scholarly journals Uniform dimension results for a family of Markov processes

Bernoulli ◽  
2018 ◽  
Vol 24 (4B) ◽  
pp. 3924-3951 ◽  
Author(s):  
Xiaobin Sun ◽  
Yimin Xiao ◽  
Lihu Xu ◽  
Jianliang Zhai
Keyword(s):  
Markov Processes ◽  
Uniform Dimension

scholarly journals Center of skew PBW extensions

2020 ◽  
Vol 30 (08) ◽  
pp. 1625-1650
Author(s):  
Oswaldo Lezama ◽  
Helbert Venegas
Keyword(s):  
Polynomial Type ◽  
Noncommutative Algebras ◽  
Skew Pbw Extensions

In this paper we compute the center of many noncommutative algebras that can be interpreted as skew [Formula: see text] extensions. We show that, under some natural assumptions on the parameters that define the extension, either the center is trivial, or, it is of polynomial type. As an application, we provided new examples of noncommutative algebras that are cancellative.

Associated prime ideals over skew PBW extensions

2020 ◽  
Vol 48 (12) ◽  
pp. 5038-5055
Author(s):  
Arturo Niño ◽  
María Camila Ramírez ◽  
Armando Reyes
Keyword(s):  
Prime Ideals ◽  
Associated Prime Ideals ◽  
Skew Pbw Extensions ◽  
Associated Prime

scholarly journals ORE AND GOLDIE THEOREMS FOR SKEW PBW EXTENSIONS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350061 ◽  
Author(s):  
Oswaldo Lezama ◽  
Juan Pablo Acosta ◽  
Cristian Chaparro ◽  
Ingrid Ojeda ◽  
César Venegas
Keyword(s):  
Commutative Rings ◽  
Polynomial Rings ◽  
Quantum Matrices ◽  
Weyl Algebras ◽  
Skew Polynomial Rings ◽  
Finite Dimensional ◽  
Quantum Version ◽  
Skew Pbw Extensions ◽  
Skew Polynomial ◽  
Finite Dimensional Lie Algebras

Many rings and algebras arising in quantum mechanics can be interpreted as skew Poincaré–Birkhoff–Witt (PBW) extensions. Indeed, Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others, are examples of skew PBW extensions. In this paper, we extend the classical Ore and Goldie theorems, known for skew polynomial rings, to this wide class of non-commutative rings. As application, we prove the quantum version of the Gelfand–Kirillov conjecture for the skew quantum polynomials.

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