关于Gorenstein FI-内射模

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英文篇名：On Gorenstein FI-injective modules 作者：陈东 ; 胡葵 英文作者：CHEN Dong;HU Kui;College of Information Science and Engineering,Chengdu University;College of Science,Southwest University of Science and Technology; 关键词：Gorenstein ; FI-内射模 ; 内射模 ; 内射维数 ; 内射包 ; 半遗传环 英文关键词：Gorenstein FI-injective module;;injective module;;injective dimension;;injective envelope;;semi-hereditary ring 中文刊名：XBSF 英文刊名：Journal of Northwest Normal University(Natural Science) 机构：成都大学信息科学与工程学院;西南科技大学理学院; 出版日期：2019-05-15 出版单位：西北师范大学学报(自然科学版) 年：2019 期：v.55;No.206 基金：国家自然科学基金资助项目(11671283);; 成都大学青年基金资助项目(2018XZA08) 语种：中文; 页：XBSF201903003 页数：5 CN：03 ISSN：62-1087/N 分类号：13-17

摘要

引入了Gorenstein FI-内射模,它是介于内射模和Gorenstein内射模之间的一种特殊模类.讨论了Gorenstein FI-内射模的诸多性质,给出了Gorenstein FI-内射模是内射模的一个充分条件,并用Gorenstein FI-内射模刻画了半遗传环.最后,定义了Gorenstein FI-内射维数,给出了Gorenstein FI-内射(预)包存在的一个充分条件.
        The concept of Gorenstein FI-injective modules is introduced,which is a particular class between injective and Gorenstein injective modules.Some properties of Gorenstein FI-injective modules are discussed,a sufficient condition for Gorenstein FI-injective module to be injective is given,and semi-hereditary rings are characterized in terms of Gorenstein FI-injective modules.Finally,Gorenstein FI-injective dimension is defined,and a sufficient condition for the existence of Gorenstein FI-injective(pre)envelope is given.

引文

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