| 摘要: |
| 设A是有足够多投射对象和足够多内射对象的正合范畴.本文研究了A的整体Gorenstein维数和A中的Gorenstein导出函子.利用同调的方法，证明了：如果A有可数直和与可数直积，那么sup{GpdM|M ∈ A}=sup{GidM|M ∈ A}；对A中的对象M，N，若GpdM < ∞，GidN < ∞，则对任意的i ≥ 0，ExtGPi（M，N）~=ExtGIi（M，N）. |
| 关键词: 正合范畴 整体Gorenstein维数 Gorenstein导出函子 |
| DOI： |
| 分类号:O154.2 |
| 基金项目:国家自然科学基金资助项目（11861055）；常州工学院科研项目（E3-6107-17-019）. |
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| GLOBAL GORENSTEIN DIMENSION OF EXACT CATEGORIES |
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GUO Jing-ge1, WANG Jun-fu2, ZHAO Ren-yu1
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1.College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China;2.School of Science, Changzhou Institute of Technology, Changzhou 213032, China
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| Abstract: |
| Let A be an exact category with enough projectives and injectives. In this paper, we study global Gorenstein dimension of A and Gorenstein derived funtors in A. By using homological methods, it is shown that if A has countable direct sums and countable direct products, then sup{GpdM|M ∈ A}=sup{GidM|M ∈ A}. We also prove that ExtGPi(M, N)~=ExtGIi(M, N) for any objects M, N in A with GpdM < ∞, GidN < ∞ and any i ≥ 0. |
| Key words: exact category global Gorenstein dimension Gorenstein derived functor |
