F-regularity relative to modules
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Abstract:
In this paper we will generalize some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .
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f-regularity relative to modules
in this paper we will generalize some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .
full textRelative (co)homology of $F$-Gorenstein modules
We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.
full textrelative (co)homology of $f$-gorenstein modules
we investigate the relative cohomology and relative homology theories of $f$-gorenstein modules, consider the relations between classical and $f$-gorenstein (co)homology theories.
full textThe small intersection graph relative to multiplication modules
Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...
full textRanks of modules relative to a torsion theory
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and c...
full textRelative Cotorsion Modules and Relative Flat Modules
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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Journal title
volume 3 issue 1
pages 41- 50
publication date 2015-06-01
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