[1]焦天明,杨晓燕.Ding投射模和强Ding投射模[J].江西师范大学学报(自然科学版),2015,(01):46-49.
　JIAO Tianming,YANG Xiaoyan.The Ding Projective Modules and Strongly Ding Projective Modules[J].Journal of Jiangxi Normal University:Natural Science Edition,2015,(01):46-49.
点击复制

Ding投射模和强Ding投射模()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2015年01期
页码:
46-49
栏目:
出版日期:
2015-02-10

文章信息/Info

Title:
The Ding Projective Modules and Strongly Ding Projective Modules
作者:
焦天明；杨晓燕
西北师范大学数学与统计学院,甘肃 兰州 730070
Author(s):
JIAO Tianming; YANG Xiaoyan
关键词:
Ding投射模;  强Ding投射模;  n-强Ding投射模
Keywords:
Ding projective module;  strongly Ding projective module;  n-modules classes respectively. Ding projective module;  strongly Ding projective module;  rongly Ding projective module
分类号:
O 153.3
文献标志码:
A
摘要:
给出了Ding投射模是强Ding投射模的条件,证明了i=1,2,…,m,若D-gldim(Ri)<∞,则SDP(∏i=1Ri)=DP(∏i=1Ri)当且仅当i,SDP(Ri)=DP(Ri),其中DP(R)和SDP(R)分别表示Ding投射R-模类和强Ding投射R-模类.
Abstract:
The conditions that the class of every Ding projective modules is strongly Ding projective modules are given.It is proved that if D-gldim(Ri)<∞,i=1,2,…,m,then SDP(∏i=1Ri)=DP(∏i=1Ri) if and only if SDP(Ri)=DP(Ri) for each i,where DP(R) and SDP(R) denote the classes of Ding projective R-modules classes and strongly Ding projective R-modules classes respectively.

参考文献/References:

[1]Mao Lixin,Ding Nanqing.Gorenstein FP injective and Goren-stein flat modules [J].Journal of Algebra and Its Applications,2008,7(4):491-506.
[2] Ding Nanqing,Li Yuanlin,Mao Lixin.Strongly Gorenstein flat modules [J].Journal of the Australian Mathematical Society,2009,86(3):323-338.
[3] Gillesple J.Module structures on modules over Ding-Chen rings [J].Homology,Homotopy and Applications,2010,12(1):61-73.
[4] Mahdou N,Mohammed T.When every Gorenstein projective(resp.flat)modules is strongly Gorenstein projective(resp.flat)modules [J].Communications on Pure and Applied Mathematics,2010,1(1):15-25.
[5] Anderson F W,Fuller K R.Rings and Categories of Modules [M].New York:Spring-Verlag,1992.
[6] Holm H.Gorenstein homological dimensions [J].Journal of Pure and Applied Algebra,2004,189(1):167-194.
[7] Mahdou N,Mohammed T.Strongly Gorenstein flat modules and dimensions [J].Chinese Annals of Mathematics-Series B,2011,32(4):533-548.
[8]王聪,黄福生.拟内射半模与伪内射半模[J].江西师范大学学报:自然科学版,2012,36(2):155-159.
[9] Bennis D,Mahdou N.Global Gorenstein dimensions[J].Proceedings of the American Mathematical Society,2009,138(2):461-465.
[10] Berrick A J,Keating M E.An introduction to rings and modules [M].Cambridge:Cambridge University Press,2000.
[11] Bennis D,Mahdou N.Global Gorenstein dimensions of polynomial rings and direct products of rings [J].Houston Journal of Mathematics,2009,35(4):1019-1028.
[12]刘妍平.一类特殊的Ding-模及其性质 [D].兰州:西北师范大学,2013.

备注/Memo

备注/Memo:
国家自然科学基金(11361051,11461060)
更新日期/Last Update: 1900-01-01