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TI-内射模与TI-平坦模(英文) 被引量：1

TI-Injective and TI-Flat Modules
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摘要 R是环.若对任意FGT-内射右R-模N和R-模M,Ext1(N,M)=0,则称M为TI-内射.若对任意FGT-内射右R-模N和左R-模F,Tor1(N,F)=0,则称F为TI-平坦的.主要研究TI-内射模与TI-平坦模以及它们和FGT-内射预盖与FGT-平坦预包络的关系.还利用TI-内射模与TI-平坦模以及Hom的左导出函子刻画了模和环的TI-维数. Let R be a ring.A right R-module M is called TI-injective in case Ext1（N,M）=0 for any FGT-injective right R-module N.A left R-module F is said to be TI-flat if Tor1（N,F）=0 for any FGT-injective right R-module N.TI-injective and TI-flat modules and their relations with FGT-injective （pre） covers and FGT-flat preenvelopes are studied.TI-dimensions of modules and rings in terms of these modules and left derived functors of Hom are also studied.
作者 向跃明
机构地区 湖南师范大学数学与计算机科学学院
出处 《湖南师范大学自然科学学报》 CAS 北大核心 2010年第4期3-8,共6页 Journal of Natural Science of Hunan Normal University
关键词 TI-内射模 TI-平坦模 ∏-凝聚环 TI-维数 TI-injective module TI-flat module ∏-coherent ring TI-dimension
分类号 O153.3 [理学—基础数学]
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参考文献14

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同被引文献12

  • 1ANDERSON F W, FULLER K R. Rings and categories of modules [M]. New York: Spring-Verlag, 1992.
  • 2ENOCHS E E, JENDA O M G. Relative homological algebra [ M ]. Berlin-New York:Walter de Gruyter, 2000.
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  • 4CHEATHAM T J, STONE D. R. Flat and projective character modules [J]. Proc Amcr Math Soc, 1981,81(2) :175-177.
  • 5MAO L X. Min-flat modules and rain-coherent rings [J]. Comm Algebra. 2007.35(2) :635-650.
  • 6DUAN L L, OUYANG B Y. Relative FI-injectiee and H-fiat modules [J]. Indian J Pure Appl Math, 2011,42(6) :417-441.
  • 7TRLIFAJ J. Covers, envelopes, and cotorslon theories [ R]. Lecture notes for the workshop. Homological Methods in Module Theory Cortona, September, 2000,10-16.
  • 8MAO L X, DING N Q. Envelopes and covers by modules of finite FP-injective and flat dimensions [J]. Comm Algebra, 2007,35 (3) :833-849.
  • 9CHEN J N, DING N Q. On n-coherent rings [J]. Comm Algebra, 1996,24(10) :3211-3216.
  • 10ZHOU D X. On n-coherent rings and (n,d) rings [J]. Comm Algebra, 2004,32(6) :2425-2441.

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湖南师范大学自然科学学报
2010年 第4期

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