Relative injectivity and flatness of complexes
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- Lu Bo
- Department of Mathematics Northwest Normal University
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- Liu Zhongkui
- Department of Mathematics Northwest Normal University
抄録
A complex C is said to be FR-injective (resp., FR-flat) if Ext1(D,C) = 0 (resp., $\overline{Tor}1 (C,D) = 0) for any finitely represented complex D. We prove that a complex C is FR-injective (resp., FR-flat) if and only if C is exact and Zm(C) is FR-injective (resp., FR-flat) in R-Mod for all m ∈ Z. We show that the class of FR-injective complexes is closed under direct limits and the class of FR-flat complexes is closed under direct products over any ring R. We use this result to prove that every complex have FR-flat preenvelopes and FR-injective covers.
収録刊行物
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- KODAI MATHEMATICAL JOURNAL
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KODAI MATHEMATICAL JOURNAL 36 (2), 343-362, 2013
国立大学法人 東京工業大学理学院数学系
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キーワード
詳細情報 詳細情報について
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- CRID
- 1390001205272144768
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- NII論文ID
- 130004687990
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- ISSN
- 18815472
- 03865991
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- MRID
- 3081252
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- Crossref
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可