نتایج جستجو برای: global cotorsion dimension

تعداد نتایج: 553253  

Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.

Journal: :نظریه تقریب و کاربرد های آن 0
ن طیارزاده دانشگاه آزاد واحد گچساران ایران اسمعیل حسینی دانشگاه آزاد واحد گچساران ایران َش نیک نژاد دانشگاه آزاد واحد گچساران

let r be an associative ring with identity, c(r) be the category of com-plexes of r-modules and flat(c(r)) be the class of all at complexes of r-modules. we show that the at cotorsion theory (flat(c(r)); flat(c(r))−)have enough injectives in c(r). as an application, we prove that for each atcomplex f and each complex y of r-modules, exti (f,x)= 0, whenever ris n-perfect and i > n.

2008
Driss Bennis Najib Mahdou

In this paper, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.

2005
Lixin Mao Nanqing Ding

In this paper, we introduce a dimension, called the cotorsion dimension, for modules and rings. The relations between the cotorsion dimension and other dimensions are discussed. Various results are developed, some extending known results.

Journal: :Hacettepe journal of mathematics and statistics 2022

Let $R$ be a ring, $S$ multiplicative subset of $R$. An $R$-module $M$ is said to $u$-$S$-flat ($u$- always abbreviates uniformly) if $\Tor^R_1 (M, N)$ $u$-$S$-torsion for all $R$-modules $N$. In this paper, we introduce and study the concept $S$-cotorsion module which in some way generalization notion cotorsion module. $\Ext^1_R(F,M)=0$ any $F$. This new class modules will used characterize $u...

2004
JAN TRLIFAJ

Classical tilting theory generalizes Morita theory of equivalence of module categories. The key property – existence of category equivalences between large full subcategories of the module categories – forces the representing tilting module to be finitely generated. However, some aspects of the classical theory can be extended to infinitely generated modules over arbitrary rings. In this paper,...

Journal: :Journal of Algebra and Its Applications 2009

2009
M. CORTÉS IZURDIAGA S. ESTRADA P. A. GUIL ASENSIO

We explore the interlacing between model category structures attained to classes of modules of finite X -dimension, for certain classes of modules X . As an application we give a model structure approach to the Finitistic Dimension Conjectures and present a new conceptual framework in which these conjectures can be studied. Let Λ be a finite dimensional algebra over a field k (or more generally...

2008
Driss Bennis Najib Mahdou

A ring is called n-perfect (n ≥ 0), if every flat module has projective dimension less or equal than n. In this paper, we show that the n-perfectness relate, via homological approach, some homological dimension of rings. We study n-perfectness in some known ring constructions. Finally, several examples of n-perfect rings satisfying special conditions are given.

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