引用本文:宋彦辉, 梁力.模的限制内射维数[J].西南大学学报(自然科学版),2018,40(12):94~99
【打印本页】   【HTML】   【下载PDF全文】   查看/发表评论  【EndNote】   【RefMan】   【BibTex】
←前一篇|后一篇→ 过刊浏览    高级检索
本文已被:浏览 93次   下载 84 本文二维码信息
码上扫一扫!
分享到: 微信 更多
模的限制内射维数
宋彦辉, 梁力
兰州交通大学 数理学院, 兰州 730070
摘要:
介绍并研究了限制内射模,指出Gorenstein内射模是限制内射模,但反之不然.利用限制内射模的分解进一步研究了经典的限制内射维数,给出了其新的计算办法.证明了强挠自由模的特征模是限制内射的.当限定环的条件,即splf R° < ∞时,证明了:R-模M是强挠自由模当且仅当特征模M+是限制内射的.进一步,探讨了R-模M的限制平坦维数和M+的限制内射维数之间的关系.
关键词:  限制内射模  限制内射维数  强挠自由模
DOI:10.13718/j.cnki.xdzk.2018.12.015
分类号:O154.2
基金项目:国家自然科学基金项目(11761045,11561039);兰州交通大学"百名青年优秀人才培养计划"基金资助项目;甘肃省自然科学基金项目(18JR3RA113,17JR5RA091).
Restricted Injective Dimension of Modules
SONG Yan-hui, LIANG Li
School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China
Abstract:
This paper introduces the conception of restricted injective module and points out that Gorenstein injective modules are restricted injective modules, but the opposite is not true. The classical restricted injective dimension is investigated by using resolutions with restricted injective modules, and some new methods are given to compute the restricted injective dimension. It is shown in the paper that M is a strongly torsion-free module and M+ is restricted injective. If splf R° < ∞, then M is a strongly torsion-free module if and only if M+ is restricted injective. Furthermore, the relationships between the restricted flat dimension of M and the restricted injective dimension of M+ are given.
Key words:  restricted injective module  restricted injective dimension  strongly torsion-free module
手机扫一扫看