Abstract
AbstractIn this paper, we provide a new and more general filtration to the family of noncommutative rings known as skew PBW extensions. We introduce the notion of $$\sigma $$
σ
-filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a $$\sigma $$
σ
-filtered skew PBW extension A over a ring R is a graded skew PBW extension over the homogenization of R. Using this fact, we prove that if the homogenization of R is Auslander-regular, then the homogenization of A is a domain Noetherian, Artin–Schelter regular, and A is Noetherian, Zariski and (ungraded) skew Calabi–Yau.
Publisher
Springer Science and Business Media LLC
Reference55 articles.
1. Acosta, J.P.; Lezama, O.: Universal property of skew PBW extensions. Algebra Discrete Math. 30(1), 1–12 (2015)
2. Andruskiewitsch, N., Dumas, F., Peña, H. M.: On the double of the Jordan plane. arXiv:2108.13849v1 [math.RA] (2021)
3. Artamonov, V. A.: Derivations of skew PBW extensions. Commun. Math, Stat 3(4), 449–457 (2015). https://doi.org/10.1007/s40304-015-0067-9
4. Artin, M.; Schelter, W.F.: Graded algebras of global dimension 3. Adv. Math. 66(2), 171–216 (1987)
5. Bell, A.; Goodearl, K.: Uniform rank over differential operator rings and Poincaré-Birkhoff-Witt extensions. Pac. J. Math. 131(11), 13–37 (1988)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献