منابع مشابه
Periodic Flat Modules, and Flat Modules for Finite Groups
If R is a ring of coefficients and G a finite group, then a flat RG-module which is projective as an R-module is necessarily projective as an RG-module. More generally, if H is a subgroup of finite index in an arbitrary group Γ, then a flat RΓmodule which is projective as an RH-module is necessarily projective as an RΓ-module. This follows from a generalization of the first theorem to modules o...
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Let R be a ring, M a right R-module, and n a fixed non-negative integer. M is called n-cotorsion if Extn+1 R N M = 0 for any flat right R-module N . M is said to be n-flat if ExtR M N = 0 for any n-cotorsion right R-module N . We prove that ( n n is a complete hereditary cotorsion theory, where n (resp. n) denotes the class of all n-flat (resp. n-cotorsion) right R-modules. Several applications...
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Let R be a right GF-closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorensntein flat dimensnion of R/I as a right R-module and the Gorensntein injective dimensnnion of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorensntein ring R, ...
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Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the...
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In this paper, we principally explore flat modules over a commutative ring with identity. We do this in relation to projective and injective modules with the help of derived functors like Tor and Ext. We also consider an extension of the property of flatness and induce analogies with the “special cases” occurring in flat modules. We obtain some results on flatness in the context of a noetherian...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7936