{"title":"Relative versions of depth, Ischebeck, and Chouinard formulas with respect to a semidualizing module","authors":"Maryam Salimi, Elham Tavasoli","doi":"10.1007/s40065-025-00498-z","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>R</i> be a commutative Noetherian ring, and let <i>C</i> be a semidualizing <i>R</i>-module. The present paper aims at studying some properties of <span>\\({\\textrm{Hom}_{\\textrm{R}}}(C, M)\\)</span> and <span>\\(C \\otimes _{R} M\\)</span> where <i>M</i> is a non-zero finitely generated <i>R</i>-module. Also, we investigate other versions of depth formula for relative Tor-independent modules with respect to <i>C</i>. Finally, we establish relative versions of Ischebeck and Chouinard formulas for <i>R</i>-modules of finite relative homological dimensions with respect to <i>C</i>.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"14 1","pages":"171 - 181"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-025-00498-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: 0
Abstract
Let R be a commutative Noetherian ring, and let C be a semidualizing R-module. The present paper aims at studying some properties of \({\textrm{Hom}_{\textrm{R}}}(C, M)\) and \(C \otimes _{R} M\) where M is a non-zero finitely generated R-module. Also, we investigate other versions of depth formula for relative Tor-independent modules with respect to C. Finally, we establish relative versions of Ischebeck and Chouinard formulas for R-modules of finite relative homological dimensions with respect to C.
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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