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
Abstract
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.
Journal
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- Kodai Mathematical Journal
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Kodai Mathematical Journal 36 (2), 343-362, 2013
Department of Mathematics, Tokyo Institute of Technology
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Keywords
Details 詳細情報について
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- CRID
- 1390001205272144768
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- NII Article ID
- 130004687990
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- ISSN
- 18815472
- 03865991
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- MRID
- 3081252
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed