{"title":"Rings for which general linear forms are exact zero divisors","authors":"Ayden Eddings, Adela Vraciu","doi":"arxiv-2407.16000","DOIUrl":null,"url":null,"abstract":"We investigate the standard graded $k$-algebras over a field $k$ of\ncharacteristic zero for which general linear forms are exact zero divisors. We\nformulate a conjecture regarding the Hilbert function of such rings. We prove\nour conjecture in the case when the ring is a quotient of a polynomial ring by\na monomial idea, and also in the case when the ideal is generated in degree 2\nand all but one of the generators are monomials.","PeriodicalId":501475,"journal":{"name":"arXiv - MATH - Commutative Algebra","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Commutative Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.16000","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We investigate the standard graded $k$-algebras over a field $k$ of
characteristic zero for which general linear forms are exact zero divisors. We
formulate a conjecture regarding the Hilbert function of such rings. We prove
our conjecture in the case when the ring is a quotient of a polynomial ring by
a monomial idea, and also in the case when the ideal is generated in degree 2
and all but one of the generators are monomials.
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