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2 results

  • FP-INJECTIVE COMPLEXES AND FP-INJECTIVE DIMENSION OF COMPLEXES

  • Part of
  • ZHANPING WANG, ZHONGKUI LIU
  • Journal:
    Journal of the Australian Mathematical Society / Volume 91 / Issue 2 / October 2011
    Published online by Cambridge University Press:
    25 August 2011, pp. 163-187
    Print publication:
    October 2011
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  • In this paper we extend the notion of FP-injective modules to that of complexes and characterize such complexes. We show that some characterizations similar to those for injective complexes exist for FP-injective complexes. We also introduce and study the notion of an FP-injective dimension associated to every complex of left R-modules over an arbitrary ring. We show that there is a close connection between the FP-injective dimension of complexes and flat dimension.

  • ON A DUALITY THEOREM OF WAKAMATSU

  • Part of
  • ZHAOYONG HUANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 78 / Issue 2 / October 2008
    Published online by Cambridge University Press:
    01 October 2008, pp. 343-350
    Print publication:
    October 2008
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  • Let R be a left coherent ring, S a right coherent ring and RU a generalized tilting module, with S=End(RU) satisfying the condition that each finitely presented left R-module X with ExtRi(X,U)=0 for any i≥1 is U-torsionless. If M is a finitely presented left R-module such that ExtRi(M,U)=0 for any i≥0 with (where n is a nonnegative integer), then and ExtSi(ExtRn(M,U),U)=0 for any i≥0 with . A duality is thus induced between the category of finitely presented holonomic left R-modules and the category of finitely presented holonomic right S-modules.