Skew PBW Extensions of Baer, quasi-Baer, p.p. and p.q.-rings

Reyes, Armando

doi:10.18273/revint.v33n2-2015007

Cited by 25 publications

(40 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, Σ-rigid rings are reduced rings: if B is a Σ-rigid ring and r 2 = 0 for r ∈ B, then we have the equalities 0 = rσ α (r 2 )σ α (σ α (r)) = rσ α (r)σ α (r)σ α (σ α (r)) = rσ α (r)σ α (rσ α (r)), i.e., rσ α (r) = 0 and so r = 0, that is, B is reduced (note that there exists an endomorphism of a reduced ring which is not a rigid endomorphism, see [10] for more details). With this in mind, we consider the family of injective endomorphisms Σ and the family ∆ of Σ-derivations in a skew PBW extension A of a ring R (see Proposition 2.1).…”

Section: Definition 24 ([10] Definition 32)mentioning

confidence: 99%

“…One can prove that any rigid endomorphism is injective and σ-rigid rings are reduced (see Hong et al [9]). Different properties of σ-rigid rings have been studied in the literature (see [10] and [11] for a detailed list of works). (2) σ-skew Armendariz defined by Hong et al [12]: if σ is an endomorphism of a ring B, then B is called to be σ-skew Armendariz, if whenever polynomials f = [15]: a ring B is σ-compatible, if for each a, b ∈ B, aσ(b) = 0 ⇔ ab = 0; B is said to be δ-compatible, if for each a, b ∈ B, ab = 0 ⇒ aδ(b) = 0.…”

Section: Introductionmentioning

confidence: 99%

“…In this way we continue our work of generalizing several results in the literature for Ore extensions. As a matter of fact, the notions (1), (2), (3), (4) and (5) above mentioned have been investigated for skew PBW extensions in [10], [28], [11], [29] and [23], respectively, so only the notions (6) and (7) have not considered. It is precisely the purpose of this paper to investigate these notions in the context of skew PBW extensions with a view toward quantum algebras.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Symmetry and reversibility properties for quantum algebras and skew Poincaré-Birkhoff-Witt extensions

Reyes

Jaramillo

2018

ing.cienc

Self Cite

View full text Add to dashboard Cite

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 properties transfer from a ring of coefficients to a quantum algebra or skew PBW extension over this ring. In this way we generalize several results established in the literature and consider algebras which have not been studied before. We illustrate our results with remarkable examples of theoretical physics.Key words: Symmetry; reversibility; quantum algebra; skew Poincaré-Birkhoff-Witt extension.1 Universidad Nacional de Colombia, mareyesv@unal.edu.co, https://orcid.org/0000-0002-5774-0822, Bogotá, Colombia.2 Universidad Nacional de Colombia, jcjaramilloq@unal.edu.co, Orinoquia, Colombia. Universidad EAFIT 29| Symmetry and Reversibility Properties for Quantum Algebras and Skew Poincaré-Birkhoff-Witt ExtensionsPropiedades de simetría y reversibilidad para álgebras cuánticas y extensiones torcidas de Poincaré-Birkhoff-Witt ResumenNuestro propósito en este artículo es investigar las propiedades de simetría y reversibilidad para álgebras cuánticas y extensiones PBW torcidas. Bajo ciertas condiciones mostramos que estas propiedades se transfieren de un anillo de coeficientes a un álgebra cuántica o extensión PBW torcida sobre este anillo. De esta manera generalizamos diversos resultados establecidos en la literatura, y los ampliamos a álgebras antes no estudiadas. Ilustramos nuestros resultados con ejemplos destacados de la física teórica.Palabras clave: Simetría; reversibilidad; álgebra cuántica; extensión torcida de Poincaré-Birkhoff-Witt.

show abstract

Section: Definition 24 ([10] Definition 32)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry and reversibility properties for quantum algebras and skew Poincaré-Birkhoff-Witt extensions

Reyes

Jaramillo

2018

ing.cienc

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several properties of α-rigid rings have been established in the literature (c.f. [5], [3], and see [13] for detailed references). With this definition in mind, Ouyang [10] defined weak α-rigid rings which are a generalization of α-rigid rings.…”

Section: Introductionmentioning

confidence: 99%

Skew Poincaré-Birkhoff-Witt Extensions Over Weak Σ-Rigid Rings

Reyes¹,

Suárez²

2018

FJMS

Self Cite

View full text Add to dashboard Cite

In this paper we introduce the notion of weak Σ-rigid ring which extends α-rigid rings and Σrigid rings defined for Ore extensions and skew PBW extensions, respectively. We also present the notion of weak Σ-skew Armendariz ring which extends that of α-skew Armendariz ring. In this way we generalize several results in the literature, from Ore extensions of injective type to the more general setting of skew PBW extensions.

show abstract

“…The results presented are new for skew PBW extensions and all they are similar to others existing in the literature. In this way, we continue the task of studying several properties of skew PBW extensions and its relationship with other noncommutative rings (see [1], [8], [12], [13], [17], [18], [19], [20], [22], [24] and others).…”

Section: Introductionmentioning

confidence: 99%

Some Remarks About the Cyclic Homology of Skew PBW Extensions / Algunas observaciones sobre la homología cíclica de extensiones PBW torcidas

Suárez

Villamil

2016

Cienc. En Desarro.

View full text Add to dashboard Cite

We study the cyclic homology for a class of noncommutative polynomial rings known as skew PBW extensions. We obtain explicit computations for some important families of such extensions over fields. In particular, we consider the cyclic homology of skew PBW extensions of derivation type, certain classes of Ore extensions, operator algebras, difusion algebras, quantum algebras and 3-dimensional skew polynomial algebras.Key words: Cyclic homology, Filtered rings, Skew PBW extensions. ResumenEstudiamos la homología cíclica de una clase de anillos de polinomios no conmutativos denominados extensiones PBW torcidas. Obtenemos cálculos explícitos para algunas familias importantes de este tipo de extensiones sobre cuerpos. En particular, consideramos la homología cíclica de las extensiones PBW torcidas de tipo derivación, ciertas clases de extensiones de Ore, álgebras de operadores, álgebras de difusión, álgebras cuánticas y álgebras de polinomios torcidos 3-dimensionales.

show abstract

Skew PBW Extensions of Baer, quasi-Baer, p.p. and p.q.-rings

Abstract: Abstract. The aim of this paper is to study skew Poincaré-Birkhoff-Witt extensions of Baer, quasi-Baer, p.p. and p.q.-Baer rings. Using a notion of rigidness, we prove that these properties are stable over this kind of extensions.

Cited by 25 publications

References 19 publications

Symmetry and reversibility properties for quantum algebras and skew Poincaré-Birkhoff-Witt extensions

Symmetry and reversibility properties for quantum algebras and skew Poincaré-Birkhoff-Witt extensions

Skew Poincaré-Birkhoff-Witt Extensions Over Weak Σ-Rigid Rings

Some Remarks About the Cyclic Homology of Skew PBW Extensions / Algunas observaciones sobre la homología cíclica de extensiones PBW torcidas

Contact Info

Product

Resources

About