{"title":"Ore localisation for differential graded rings; towards Goldie's theorem for differential graded algebras","authors":"","doi":"10.1016/j.jalgebra.2024.08.032","DOIUrl":null,"url":null,"abstract":"<div><div>We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to a dg-version of Goldie's theorem on prime dg-rings.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324004988","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study Ore localisation of differential graded algebras. Further we define dg-prime rings, dg-semiprime rings, and study the dg-nil radical of dg-rings. Then, we define dg-essential submodules, dg-uniform dimension, and apply all this to a dg-version of Goldie's theorem on prime dg-rings.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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