内射余分解类与投射分解类

曾月迪, 陈建龙

数学学报 ›› 2012, Vol. 55 ›› Issue (1) : 41-54.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2012, Vol. 55 ›› Issue (1) : 41-54. DOI: 10.12386/A2012sxxb0004
论文

内射余分解类与投射分解类

    曾月迪1, 陈建龙2
作者信息 +

Injectively Coresolving Classes and Projectively Resolving Classes

    Yue Di ZENG1, Jian Long CHEN2
Author information +
文章历史 +

摘要

令C是直和与直和项封闭的右R-模类. 本文讨论了关于内射余分解类与投射分解类的左(右)C-维数和左正合函子之间的关系, 并由此得到一些应用.  

Abstract

In this paper, let C be a class of right R-modules closed under isomorphisms and direct summands. The relations between left(right)C-dimensions and left exact functors are considered for an(injectively)coresolving class C or a(projectively)resolving class C. In view of those, there are some applications.  

关键词

(内射)余分解 / (投射)分解 / 维数

Key words

(injectively)coresolving / (projectively)resolving / dimensions

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曾月迪, 陈建龙. 内射余分解类与投射分解类. 数学学报, 2012, 55(1): 41-54 https://doi.org/10.12386/A2012sxxb0004
Yue Di ZENG, Jian Long CHEN. Injectively Coresolving Classes and Projectively Resolving Classes. Acta Mathematica Sinica, Chinese Series, 2012, 55(1): 41-54 https://doi.org/10.12386/A2012sxxb0004

参考文献

[1] Anderson Frank W., Fuller Kent R., Rings and Categries of Modules, Second Edition, New York: Springer-Verlag, 1992.



[2] Enochs E. E., Jenda O. M. G., Relative Homological Algebra, de Gruyter, Berlin: de Gruyter Exp. Math., 2000.



[3] Enochs E. E., Injective and flat covers, envelopes and resolvents, Israel J. Math., 1981, 39(3): 189-209.



[4] Mao L. X., Ding N. Q., FI-injective and FI-flat module, J. Algebra, 2007, 309(1): 367-385.



[5] Chen J. L., Ding N. Q., On global dimensions and E-syzygies, Algebra Colloq., 1996, 3(3): 273-276.



[6] Mao L. X., Ding N. Q., On divisible and torsionfree module, Comm. Algebra, 2008, 36(2): 708-731.



[7] Pinzon K. R., Absolutely pure covers, Comm. Algebra, 2008, 36(6): 2186-2194.



[8] Stenström B., Coherent rings and FP-injective modules, J. London Math. Soc., 1970, 2(2): 323-329.

基金

国家自然基金资助项目(10871042); 高等学校博士学科点专项科研基金(200802860024)

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