| 粘合、倾斜同调维数与高维Auslander-Reiten理论 |
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| 引用本文： | 付雪荣,姚海楼. 粘合、倾斜同调维数与高维Auslander-Reiten理论[J]. 数学研究及应用, 2020, 40(3): 263-274 |
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| 作者姓名： | 付雪荣 姚海楼 |
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| 作者单位： | 菏泽学院数学与统计学院, 山东, 荷泽 274015;北京工业大学应用数理学院, 北京 100124 |
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| 基金项目： | 国家自然科学基金(Grant No.11671126). |
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| 摘 要： | 本文主要研究阿贝尔范畴粘合$(mathscr{A}, mathscr{B}, mathscr{C})$中$mathscr{A}$, $mathscr{B}$与$mathscr{C}$之间的倾斜同调维数关系. 特别地,对遗传的阿贝尔范畴$mathscr{B}$,给出了粘合$(mathscr{A}, mathscr{B}, mathscr{C})$中的范畴之间的$n$-几乎可裂序列间的联系.
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| 关 键 词： | 粘合 倾斜同调维数 $n$-几乎可裂序列 |
| 收稿时间： | 2019-01-16 |
| 修稿时间： | 2019-10-29 |
Recollements, Tilting Homological Dimensions and Higher-Dimensional Auslander-Reiten Theory |
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| Xuerong FU,Hailou YAO. Recollements, Tilting Homological Dimensions and Higher-Dimensional Auslander-Reiten Theory[J]. Journal of Mathematical Research with Applications, 2020, 40(3): 263-274 |
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| Authors: | Xuerong FU Hailou YAO |
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| Affiliation: | College of Mathematics and Statistics, Heze University, Shandong 274015, P. R. China; College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China |
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| Abstract: | In this paper we mainly investigate the behavior of tilting homological dimensions of the categories involved in the recollement of abelian categories $(mathscr{A}, mathscr{B}, mathscr{C})$. In particular, when abelian category $mathscr{B}$ is hereditary, we give the connections between $n$-almost split sequences in the categories of $(mathscr{A}, mathscr{B}, mathscr{C})$. |
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| Keywords: | recollement tilting homological dimension $n$-almost split sequence |
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