| 关于Gorenstein投射复形的进一步研究 |
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| 引用本文： | 张齐,刘静.关于Gorenstein投射复形的进一步研究[J].阜阳师范学院学报(自然科学版),2010,27(4). |
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| 作者姓名： | 张齐 刘静 |
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| 作者单位： | 安徽大学,数学科学学院,安徽,合肥,230039 |
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| 基金项目： | 安徽大学博士点基金项目(200803570003)资助 |
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| 摘 要： | Enochs E和Garcia Rozas J R在"Gorenstein Injective and Projective Complexes"一文中证明了在n-Gorenstein环R上,若左R-模复形C为Gorenstein投射复形当且仅当它的每一项左R-模Cm为Gorenstein投射模。弱化了此结论的必要性条件,得到在任意环R上,若左R-模复形C为Gorenstein投射复形,则它的每一项左R-模Cm为Gorenstein投射模。并且最后给出Gorenstein投射复形C与任意投射复形上合冲L的关系,即Exti(C,L)=0。
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| 关 键 词： | Gorenstein投射复形 投射复形 Gorenstein投射模 上合冲 |
Further study on Gorenstein projective complexes |
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| ZHANG Qi,LIU Jing.Further study on Gorenstein projective complexes[J].Journal of Fuyang Teachers College:Natural Science,2010,27(4). |
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| Authors: | ZHANG Qi LIU Jing |
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| Institution: | ZHANG Qi,LIU Jing(School of Mathematical Sciences,Anhui University,Hefei Anhui 230039,China) |
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| Abstract: | In paper of Gorenstien injective and projective complexes,Enochs E and Garcia Rozas J R show that over n-Gorenstein ring R,a complex C of left R-module is Gorenstein projective if and only if Cm is Gorenstein projective in left R-module for allm∈Z.In this paper,we weaken the necessary conditions for this conclusion and prove that over an arbitrary ring R,a complex C of left R-module is Gorenstein projective,then Cm is Gorenstein projective in left R-module for all m∈Z.At last,we show the relationship between Gorenstein projective complex C and the cosyzygy of projective complex L,i.e.Exti(C,L)=0. |
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| Keywords: | gorenstein projective complexes projective complexes gorenstein projective modules cosyzygy |
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