Relative FI-injective and FI-flat modules

Luling Duan () and Baiyu Ouyang
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Luling Duan: Guangxi College of Education
Baiyu Ouyang: Hunan Norma University

Indian Journal of Pure and Applied Mathematics, 2011, vol. 42, issue 6, 417-441

Abstract: Abstract Let R be a ring, n a fixed nonnegative integer and FP n (F n ) the class of all left (right) R-modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module F) is called n-FI-injective (resp., n-FI-flat) if Ext 1(N,M) = 0 (resp., Tor 1(F,N) = 0) for any N ∈ FP n . It is shown that a left R-module M over any ring R is n-FI-injective if and only if M is a kernel of an FP n -precover f: A → B with A injective. For a left coherent ring R, it is proven that a finitely presented right R-module M is n-FI-flat if and only if M is a cokernel of an F n -preenvelope K → F of a right R-module K with F projective if and only if M ∈⊥ F n . These classes of modules are used to construct cotorsion theories and to characterize the global dimension of a ring.

Keywords: FP-injective dimension; n-FI-injective module; n-FI-flat module; (Pre)envelope; (Pre)cover (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s13226-011-0027-3

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