Acta mathematica scientia, Series B >
IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS
Received date: 2011-08-27
Revised date: 2012-05-16
Online published: 2012-11-20
Supported by
This research was supported by National Natural Science Foundation of China (10961021, 11001222).
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., IFn) 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 IFn-preenvelope, (IFn, IFn ) is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id(RR) ≤n, (IIn, IIn ) is a perfect cotorsion theory. This generalizes and improves the earlier work (J. Algebra 242 (2001), 447-459). Finally, some applications are given.
LU Bo , LIU Zhong-Kui . IFP-FLAT DIMENSIONS AND IFP-INJECTIVE DIMENSIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(6) : 2085 -2095 . DOI: 10.1016/S0252-9602(12)60161-1
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