| G_C-同调维数 |
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| 引用本文： | 方桂英,黄朝凌.G_C-同调维数[J].湖南师范大学自然科学学报,2012,35(1):5-8. |
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| 作者姓名： | 方桂英 黄朝凌 |
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| 作者单位： | 江西农业大学理学院,中国南昌,330045 |
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| 基金项目： | 江西农业大学自然科学基金资助项目 |
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| 摘 要： | 研究Gc-同调维数.首先考虑了Gc-同调维数与经典同调维数的关系；考虑了Gc-投射维数的换环定理,给出了经典第二换环定理的一个推广；定义了任意交换环R的有限GC-投射维数和模的Tc-平坦维数,探讨了前者与有限Pc-投射维数的关系,后者与模的Gc-平坦维数的关系；最后,研究了短正合列Gc-同调维数的关系.
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| 关 键 词： | 同调维数 Gc-投射模 Pc-内射模 换环定理 |
Gc-Homological Dimensions |
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| FANG Gui-ying
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HUANG Chao-ling.Gc-Homological Dimensions[J].Journal of Natural Science of Hunan Normal University,2012,35(1):5-8. |
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| Authors: | FANG Gui-ying HUANG Chao-ling |
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| Institution: | (College of Science,Jiangxi Agricultural University,Nanchang 330035,China) |
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| Abstract: | The GC-homological dimensions are investigated.Firstly,the relation between the GC-homological dimensions and classical homological dimensions is considered.Secondly,the change of rings theorem on GC-projective dimensions is studied.One of classical results is generalized.Thirdly,the notions of finitistic GC-projective dimension FGCPD(R) of the ring R and TC-flat dimension TC-fdR(M) of R-module M are given.It is proved that FGCPD(R)=FPCD(R) and TC-fdR(M) ≤GC-fdR(M).Finally,the ralation of GC-homological dimensions of short exact sequence is investigated. |
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| Keywords: | homological algebra GC-projective module GC-injective module change of rings theorem |
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