{"title":"纯空心模块和纯升降模块","authors":"Khawla Ahmed, Nuhad S. Al. Mothafar","doi":"10.24996/ijs.2024.65.3.32","DOIUrl":null,"url":null,"abstract":" Let be a commutative ring with identity, and be a unitary left R-module. In this paper we, introduce and study a new class of modules called pure hollow (Pr-hollow) and pure-lifting (Pr-lifting). We give a fundamental, properties of these concept. also, we, introduce some conditions under which the quotient and direct sum of Pr-lifting modules is Pr-lifting.","PeriodicalId":14698,"journal":{"name":"Iraqi Journal of Science","volume":"51 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pure-Hollow Modules and Pure-Lifting Modules\",\"authors\":\"Khawla Ahmed, Nuhad S. Al. Mothafar\",\"doi\":\"10.24996/ijs.2024.65.3.32\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" Let be a commutative ring with identity, and be a unitary left R-module. In this paper we, introduce and study a new class of modules called pure hollow (Pr-hollow) and pure-lifting (Pr-lifting). We give a fundamental, properties of these concept. also, we, introduce some conditions under which the quotient and direct sum of Pr-lifting modules is Pr-lifting.\",\"PeriodicalId\":14698,\"journal\":{\"name\":\"Iraqi Journal of Science\",\"volume\":\"51 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Iraqi Journal of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24996/ijs.2024.65.3.32\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Earth and Planetary Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iraqi Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24996/ijs.2024.65.3.32","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Earth and Planetary Sciences","Score":null,"Total":0}
引用次数: 0
摘要
假设是一个具有同一性的交换环，并且是一个单元左 R 模块。在本文中，我们引入并研究了一类新的模块，称为纯空心模块（Pr-hollow）和纯提升模块（Pr-lifting）。我们给出了这些概念的基本性质。此外，我们还介绍了一些条件，在这些条件下，Pr-lifting 模块的商和直接和是 Pr-lifting。
Let be a commutative ring with identity, and be a unitary left R-module. In this paper we, introduce and study a new class of modules called pure hollow (Pr-hollow) and pure-lifting (Pr-lifting). We give a fundamental, properties of these concept. also, we, introduce some conditions under which the quotient and direct sum of Pr-lifting modules is Pr-lifting.
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