{"title":"Homogenized skew PBW extensions","authors":"Héctor Suárez, Armando Reyes, Yésica Suárez","doi":"10.1007/s40065-022-00410-z","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(\\sigma \\)</span>-filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a <span>\\(\\sigma \\)</span>-filtered skew PBW extension <i>A</i> over a ring <i>R</i> is a graded skew PBW extension over the homogenization of <i>R</i>. Using this fact, we prove that if the homogenization of <i>R</i> is Auslander-regular, then the homogenization of <i>A</i> is a domain Noetherian, Artin–Schelter regular, and <i>A</i> is Noetherian, Zariski and (ungraded) skew Calabi–Yau.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 1","pages":"247 - 263"},"PeriodicalIF":0.9000,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-022-00410-z.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-022-00410-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
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.
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.
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