Strongly J-n-Coherent rings

IF 0.5 Q3 MATHEMATICS International Electronic Journal of Algebra Pub Date : 2023-10-28 DOI:10.24330/ieja.1411161
Zhanmin Zhu
{"title":"Strongly J-n-Coherent rings","authors":"Zhanmin Zhu","doi":"10.24330/ieja.1411161","DOIUrl":null,"url":null,"abstract":"Let $R$ be a ring and $n$ a fixed positive integer. A right $R$-module $M$ is called strongly $J$-$n$-injective if every $R$-homomorphism from an $n$-generated small submodule of a free right $R$-module $F$ to $M$ extends to a homomorphism of $F$ to $M$; a right $R$-module $V$ is said to be strongly $J$-$n$-flat, if for every $n$-generated small submodule $T$ of a free left $R$-module $F$, the canonical map $V\\otimes T\\rightarrow V\\otimes F$ is monic; a ring $R$ is called left strongly $J$-$n$-coherent if every $n$-generated small submodule of a free left $R$-module is finitely presented; a ring $R$ is said to be left $J$-$n$-semihereditary if every $n$-generated small left ideal of $R$ is projective. We study strongly $J$-$n$-injective modules, strongly $J$-$n$-flat modules and left strongly $J$-$n$-coherent rings. Using the concepts of strongly $J$-$n$-injectivity and strongly $J$-$n$-flatness of modules, we also present some characterizations of strongly $J$-$n$-coherent rings and $J$-$n$-semihereditary rings.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"226 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24330/ieja.1411161","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

Let $R$ be a ring and $n$ a fixed positive integer. A right $R$-module $M$ is called strongly $J$-$n$-injective if every $R$-homomorphism from an $n$-generated small submodule of a free right $R$-module $F$ to $M$ extends to a homomorphism of $F$ to $M$; a right $R$-module $V$ is said to be strongly $J$-$n$-flat, if for every $n$-generated small submodule $T$ of a free left $R$-module $F$, the canonical map $V\otimes T\rightarrow V\otimes F$ is monic; a ring $R$ is called left strongly $J$-$n$-coherent if every $n$-generated small submodule of a free left $R$-module is finitely presented; a ring $R$ is said to be left $J$-$n$-semihereditary if every $n$-generated small left ideal of $R$ is projective. We study strongly $J$-$n$-injective modules, strongly $J$-$n$-flat modules and left strongly $J$-$n$-coherent rings. Using the concepts of strongly $J$-$n$-injectivity and strongly $J$-$n$-flatness of modules, we also present some characterizations of strongly $J$-$n$-coherent rings and $J$-$n$-semihereditary rings.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
强 J-n 相干环
让 $R$ 是一个环,$n$ 是一个固定的正整数。如果从自由右$R$模块$F$的一个$n$生成的小子模块到$M$的每一个$R$同构都扩展到$F$到$M$的同构,那么一个右$R$模块$M$被称为强$J$-$n$内含;如果对于自由左$R$模块$F$的每一个$n$生成的小子模块$T$来说,规范映射$V\otimes T\rightarrow V\otimes F$是一元的,那么一个右$R$模块$V$可以说是强$J$-$n$平坦的;如果自由左 $R$ 模块的每个 $n$ 生成的小子模块都是有限呈现的,那么环 $R$ 称为强左 $J$-$n$ 相干;如果环 $R$ 的每个 $n$ 生成的小左理想都是投影的,那么环 $R$ 称为左 $J$-$n$ 半遗传。我们研究强$J$-$n$注入模块、强$J$-$n$平模块和左强$J$-$n$相干环。利用模块的强 $J$-$n$ 插入性和强 $J$-$n$ 平面性概念,我们还提出了强 $J$-$n$ 相干环和 $J$-$n$ 半遗传环的一些特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
0.90
自引率
16.70%
发文量
36
审稿时长
36 weeks
期刊介绍: The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.
期刊最新文献
Computational methods for $t$-spread monomial ideals Normality of Rees algebras of generalized mixed product ideals Strongly J-n-Coherent rings Strongly Graded Modules and Positively Graded Modules which are Unique Factorization Modules The structure of certain unique classes of seminearrings
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1