[1]徐龙玉,万吉湘,王芳贵.关于ZP-内射维数及ZP-平坦维数[J].江西师范大学学报(自然科学版),2016,40(02):200-203.
　XU Longyu,WAN Jixiang,WANG Fanggui.On ZP-Injective Dimensions and ZP-Flat Dimensions[J].Journal of Jiangxi Normal University:Natural Science Edition,2016,40(02):200-203.
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关于ZP-内射维数及ZP-平坦维数()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年02期
页码:
200-203
栏目:
出版日期:
2016-03-25

文章信息/Info

Title:
On ZP-Injective Dimensions and ZP-Flat Dimensions
作者:
徐龙玉;万吉湘;王芳贵
1.西南科技大学理学院,四川 绵阳 621010; 2.绵阳师范学院数学与计算机科学学院,四川 绵阳 621000; 3.四川师范大学数学与软件科学学院,四川 成都 610068
Author(s):
XU Longyu; WAN Jixiang; WANG Fanggui
1.College of Science,Southwest University of Science and Technology,Mianyang Sichuan 621010,China; 2.College of Mathematics and Computer Science,Mianyang Normal University,Mianyang Sichuan 621010,China; 3.College of Mathematics and Software Science,Sichuan Normal University,Chengdu Sichuan 610068,China
关键词:
ZP-内射模;  ZP-内射维数;  ZP-平坦模;  ZP-平坦维数
Keywords:
ZP-injective modules;  ZP-injective dimension;  ZP-flat modules;  ZP-flat dimension
分类号:
O 153.3; O 154
文献标志码:
A
摘要:
给出了ZP-内射维数以及ZP-平坦维数的定义,揭示了左ZP-内射维数l.zp.ID(R)=0及右ZP-平坦维数r.zp.FD(R)=0的环,即它们为非奇异环,并给出等价描述.讨论了环R的左ZP-内射维数l.zp.ID(R)≤n以及环R的右ZP-平坦维数r.zp.FD(R)≤n的等价刻画,证明了环R上的模类ZPI若满足单同态的上核封闭且l.zp.ID(R)< 䥺SymboleB@ ,则l.zp.ID(R)=r.zp.FD(R)=l.zp-id(RR),并证明ZP-内射左R-模的商模是ZP-内射模当且仅当模类ZPI满足单同态的上核封闭且l.zp.ID(R)≤1.
Abstract:
The notions of the ZP-injective dimensions and the ZP-flat dimensions are defined.It is shown that a ring R is left nonsingular if and only if l.zp.ID(R)=0 if and only if r.zp.FD(R)=0.Then the equivalent statements of l.zp.ID(R)≤n and r.zp.FD(R)≤n are studied.If ZPI is closed under cokernel of any monomorphism and l.zp.ID(R)<∞,then l.zp.ID(R)=r.zp.FD(R)=l.zp-id(RR).Finally,it is proved that every quotient module of a ZP-injective left R-module is ZP-injective if and only if ZPI is closed under cokernel of any monomorphisms and l.zp.ID(R)≤1.

参考文献/References:

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备注/Memo

备注/Memo:
基金项目:国家自然科学基金(11171240)资助项目.
更新日期/Last Update: 1900-01-01