| 李瑞婷,杨 刚,王小青.Clean-正合和Clean-导出范畴[J].数学年刊A辑,2019,40(3):307~324 |
| Clean-正合和Clean-导出范畴 |
| Clean Exactness and Derived Categories |
| Received:June 02, 2017 Revised:September 12, 2018 |
| DOI：10.16205/j.cnki.cama.2019.0023 |
| 中文关键词: Clean exact complexes, Clean projective modules, Clean injective mo-dules, Clean derived categories |
| 英文关键词:Clean exact complexes, Clean projective modules, Clean injective mo-dules, Clean derived categories |
| 基金项目:本文受到国家自然科学基金(No.11561039,No.11761045)和甘肃省自然科学基金(No.17JR5RA091)的资助. |
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| 中文摘要: |
| 在交换环$R$上, 引入了Clean{-}正合以及Clean{-}导出范畴的概念,
分别给出了Clean{-}短正合列和Clean{-}正合复形的等价刻画, 研究了Clean{-}导出范畴的性质.
特别地, 证明了有界Clean{-}导出范畴可以实现为特殊的同伦范畴. |
| 英文摘要: |
| Over a commutative ring, the notions of clean exactness and clean derived categories are introduced,
the equivalent characterizations of clean exactness for short exact sequences and exact complexes are given,
and the properties of clean derived categories are investigated. In particular, it is proved
that bounded clean derived categories can be realized as certain homotopy categories. |
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