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

2017 ◽  
pp. 157-178 ◽  
Author(s):  
Armando Reyes ◽  
Héctor Suárez
Keyword(s):  
Universal Enveloping Algebras ◽  
Noncommutative Rings ◽  
Enveloping Algebras ◽  
Ore Extensions ◽  
Skew Pbw Extensions

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 propositions established for Ore extensions and present new results for several noncommutative rings which can not be expressed as Ore extensions (universal enveloping algebras, diffusion algebras, and others).

scholarly journals Some remarks about minimal prime ideals of skew Poincaré-Birkhoff-Witt extensions

2020 ◽  
Vol 30 (2) ◽  
pp. 207-229
Author(s):  
A. Niño ◽  
◽  
A. Reyes ◽  
Keyword(s):  
Prime Ideals ◽  
Noncommutative Rings ◽  
Polynomial Type ◽  
Ore Extensions ◽  
Skew Pbw Extensions ◽  
Minimal Prime

In this paper, we characterize the minimal prime ideals of skew PBW extensions over several classes of rings. We unify different results established in the literature for Ore extensions, and extend all of them to a several families of noncommutative rings of polynomial type which cannot be expressed as these extensions.

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

2020 ◽  
Vol 54 (1) ◽  
pp. 39-63
Author(s):  
Mohamed Louzari ◽  
Armando Reyes
Keyword(s):  
Commutative Rings ◽  
Prime Ideals ◽  
Noncommutative Rings ◽  
Polynomial Type ◽  
Ore Extensions ◽  
Skew Pbw Extensions ◽  
Minimal Prime

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 of our treatment, the results established here generalize those corresponding for commutative rings and Ore extensions of injective type. In this way, we present new results for several noncommutative rings of polynomial type not considered before in the literature.

scholarly journals Universal enveloping algebras of Poisson Ore extensions

2015 ◽  
Vol 143 (11) ◽  
pp. 4633-4645 ◽  
Author(s):  
Jiafeng Lü ◽  
Xingting Wang ◽  
Guangbin Zhuang
Keyword(s):  
Universal Enveloping Algebras ◽  
Enveloping Algebras ◽  
Ore Extensions

Skew Poincaré–Birkhoff–Witt extensions over weak compatible rings

2019 ◽  
Vol 19 (12) ◽  
pp. 2050225 ◽  
Author(s):  
Armando Reyes ◽  
Héctor Suárez
Keyword(s):  
Algebraic Geometry ◽  
Theoretical Physics ◽  
Quantum Algebras ◽  
Noncommutative Rings ◽  
Noncommutative Algebraic Geometry ◽  
Ore Extensions ◽  
Skew Pbw Extensions ◽  
Weak Notion

In this paper, we introduce weak [Formula: see text]-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 geometry and some quantum algebras of theoretical physics. As a consequence of our treatment, we unify and extend results in the literature about Ore extensions and skew PBW extensions over compatible 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.

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