均匀化偏斜PBW扩展

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2022-12-09 DOI:10.1007/s40065-022-00410-z

Héctor Suárez, Armando Reyes, Yésica Suárez

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引用次数: 1

摘要

在本文中，我们对称为偏斜PBW扩展的非对易环族提供了一种新的、更一般的过滤。我们引入了滤斜PBW扩张的概念，并研究了这些代数的一些同调性质。我们证明了环R上的\（\∑\）滤波斜PBW扩张a的均匀化是R的均匀化上的分级斜PBW扩展。利用这个事实，我们证明了如果R的均匀性是Auslander正则，那么a的均匀性就是域Noetherian，Artin–Schelter正则，并且a是Noetheriian，Zariski和（未分级）斜Calabi–Yau。

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Homogenized skew PBW extensions

In 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 \(\sigma \)-filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a \(\sigma \)-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.

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.