{"title":"Ideal cotorsion pairs over one point extensions","authors":"Hai-yan Zhu, Ben-jun Du, Qi-kai Wang","doi":"10.1007/s11766-022-4375-z","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>R</i>[<i>P</i>] be the one point extension of a <i>k</i>-algebra <i>R</i> by a projective <i>R</i>-module <i>P</i>. We prove that the extension of a complete ideal cotorsion pair in <i>R</i>-Mod is still a complete ideal cotorsion pair in <i>R</i>[<i>P</i>]-Mod. As an application, it is obtainable that the operation (−)<sub><i>m</i></sub> [<i>P</i>] satisfies the so-called distributive law relating the operations of products and extensions of ideals under appropriate conditions.</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"37 2","pages":"213 - 227"},"PeriodicalIF":1.3000,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-022-4375-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let R[P] be the one point extension of a k-algebra R by a projective R-module P. We prove that the extension of a complete ideal cotorsion pair in R-Mod is still a complete ideal cotorsion pair in R[P]-Mod. As an application, it is obtainable that the operation (−)m [P] satisfies the so-called distributive law relating the operations of products and extensions of ideals under appropriate conditions.
期刊介绍：
Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects.
The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry.
Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.
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