| 强Gorenstein投射和内射复形(英文) |
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| 引用本文： | 张东东,欧阳柏玉. 强Gorenstein投射和内射复形(英文)[J]. 湖南师范大学自然科学学报, 2012, 0(4): 1-5 |
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| 作者姓名： | 张东东 欧阳柏玉 |
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| 作者单位： | 浙江师范大学数理与信息工程学院;湖南师范大学数学与计算机科学学院 |
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| 基金项目： | 国家自然科学基金资助项目(10901141) |
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| 摘 要： | 分别研究了Gorenstein投射和内射复形的特殊情况:强Gorenstein投射复形和强Gorenstein内射复形.证明了复形C是Gorenstein投射复形当且仅当它是强Gorenstein投射复形的直和项.同时,证明了若R在左Noetheri-an环下,下有界复形C是强Gorenstein内射复形当且仅当C是正合的且每一项Ci是强Gorenstein内射R-模.
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| 关 键 词： | 强Gorenstein投射(内射)复形 Gorenstein投射(内射)复形 |
Strongly Gorenstein Projective and Injective Complexes |
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| Affiliation: | ZHANG Dong-dong1,2,OUYANG Bai-yu2(1.Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China;2.College of Mathematics and Computer Science,Hunan Normal University,Changsha 410081,China) |
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| Abstract: | A special case of Gorenstein projective,and injective complexes,which are called strongly Gorenstein projective and injective complexes,are studied respectively.It is proved that a complex C is a Gorenstein projective if and only if it is a direct summand of a strongly Gorenstein projective complex.Meanwhile,it is shown that,over a left Noetherian ring,a bounded below complex C of left R-modules is strongly Gorenstein injective if and only if C is an exact sequence and Ci is a strongly Goren-stein injective R-module for all i∈Z. |
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| Keywords: | strongly Gorenstein projective(injective) complex Gorenstein projective(injective)complex |
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