Skew PBW extensions over symmetric rings

Reyes, Armando; Suárez, Héctor

doi:10.12958/adm1767

Cited by 4 publications

(2 citation statements)

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“…Definition 4. Let R be a ring, Σ be a finite family of endomorphism of R, and ∆ be a finite family of Σ-derivations of R. ( Some examples of skew PBW extensions over (Σ, ∆)-compatible rings include PBW extensions, some operator algebras, the class of diffusion algebras, quantizations of Weyl algebras, the family of 3-dimensional skew polynomial algebras, and other families of noncommutative algebras having PBW bases (see [61,63,64]). We present a new example of a skew PBW extension over a Σ-compatible ring.…”

Section: Definition 3 ([17 Section 3]) Ifmentioning

confidence: 99%

On Σ-skew reflexive-nilpotents-property for rings

Suárez,

Higuera,

Reyes

2024

ADM

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In this paper, we study the reflexive-nilpotents-property (briefly, RNP) for skew PBW extensions. With this aim, we introduce the Σ-skew CN and Σ-skew reflexive (RNP) rings. Under conditions of compatibility, we investigate the transfer of there flexive-nilpotents-property from a ring of coefficients to a skew PBW extension. We also consider this property for localizations on these families of noncommutative rings. Our results extend those corresponding presented by Bhattacharjee [9].

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Section: Definition 3 ([17 Section 3]) Ifmentioning

confidence: 99%

On Σ-skew reflexive-nilpotents-property for rings

Suárez,

Higuera,

Reyes

2024

ADM

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“…Thinking in the context of skew PBW extensions, Hashemi et al [41] and Reyes and Suárez [94] introduced independently the (Σ, ∆)-compatible rings as a natural generalization of (σ, δ)-compatible rings. Examples, ring and module theoretic properties of these structures can be found in [40,42,43,73,91,97].…”

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confidence: 99%

On Weak Annihilators and Nilpotent Associated Primes of Skew PBW Extensions

Higuera¹,

Reyes²

2022

Preprint

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We investigate the notions of weak annihilator and nilpotent associated prime defined by Ouyang and Birkenmeier [82] in the setting of noncommutative rings having PBW bases. We extend several results formulated in the literature concerning annihilators and associated primes of commutative rings and skew polynomial rings to a more general setting of algebras not considered before. We exemplify our results with families of algebras appearing in the theory of enveloping algebras, differential operators on noncommutative spaces, noncommutative algebraic geometry, and theoretical physics. Finally, we present some ideas for future research.

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