IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS

doi:10.1016/S0252-9602(12)60161-1

Abstract

Abstract:

In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd(M) =IFP-id(M+) and IFP-fd(M⁺)=IFP-id(M) for any R-module M over any ring R. Let IIn (resp., IF_n) be the class of all left (resp., right) R-modules of IFP-injective (resp., IFP-flat) dimension at most n. We prove that every right R-module has an IF_n-preenvelope, (IF_n, IF_n ) is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id(_RR) ≤n, (II_n, II_n ) is a perfect cotorsion theory. This generalizes and improves the earlier work (J. Algebra 242 (2001), 447-459). Finally, some applications are given.

Key words: IFP-flat dimension, IFP-injective dimension, Pre (Cover), Pre (Envelope), Cotorsion theory, IFP-cotorsion module

CLC Number:

16D50

LU Bo, LIU Zhong-Kui. IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS[J].Acta mathematica scientia,Series B, 2012, 32(6): 2085-2095.

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