On Cofinitely Lifting Modules

doi:10.1142/S1005386710000635

	On Cofinitely Lifting Modules
	Wang, Yongduo; Wu, Dejun
	2010-12
发表期刊	ALGEBRA COLLOQUIUM
ISSN	1005-3867
卷号	17 期号:4 页码:659-666
摘要	Let R be a ring and M a right R-module. M is called a cofinitely lifting module if for any cofinite submodule N of M, there exists a direct summand K of M such that K <= N and N/K << M/K. It is proved that every cofinite direct summand of a cofinitely lifting module is cofinitely lifting. For a cofinitely lifting module M and a fully invariant submodule N of M, we show that M/N is also cofinitely lifting. We prove that a duo module M - M(1) circle plus M(2) is cofinitely lifting if M(1) and M(2) are both cofinitely lifting. Let M = M(1) circle plus M(2) be an amply supplemented module. It is shown that if M(1) and M(2) are both cofinitely lifting and relatively cofinitely small projective and M(1) is cofinitely pseudo-M(2)-projective (or M(2) is cofinitely pseudo-M(1)-projective), then M is cofinitely lifting.
关键词	cofinite submodule cofinitely lifting module fully invariant submodule
DOI	10.1142/S1005386710000635
收录类别	SCI ; SCIE
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000282743500013
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计	被引频次：2[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://ir.lut.edu.cn/handle/2XXMBERH/35174
专题	材料科学与工程学院兰州理工大学
通讯作者	Wang, Yongduo
作者单位	Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Peoples R China
第一作者单位	材料科学与工程学院
通讯作者单位	材料科学与工程学院
第一作者的第一单位	材料科学与工程学院
推荐引用方式 GB/T 7714	Wang, Yongduo,Wu, Dejun. On Cofinitely Lifting Modules[J]. ALGEBRA COLLOQUIUM,2010,17(4):659-666.
APA	Wang, Yongduo,&Wu, Dejun.(2010).On Cofinitely Lifting Modules.ALGEBRA COLLOQUIUM,17(4),659-666.
MLA	Wang, Yongduo,et al."On Cofinitely Lifting Modules".ALGEBRA COLLOQUIUM 17.4(2010):659-666.