Relative injectivity and flatness of complexes

DOI
  • Lu Bo
    Department of Mathematics Northwest Normal University
  • 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

キーワード

詳細情報 詳細情報について

  • CRID
    1390001205272144768
  • NII論文ID
    130004687990
  • DOI
    10.2996/kmj/1372337523
  • ISSN
    18815472
    03865991
  • MRID
    3081252
  • 本文言語コード
    en
  • データソース種別
    • JaLC
    • Crossref
    • CiNii Articles
  • 抄録ライセンスフラグ
    使用不可

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