منابع مشابه
Sigma-cotorsion Modules over Valuation Domains
We give a characterization of Σ-cotorsion modules over valuation domains in terms of descending chain conditions on certain chains of definable subgroups. We prove that pure submodules, direct products and modules elementarily equivalent to a Σ-cotorsion module are again Σ-cotorsion. Moreover, we describe the structure of Σ-cotorsion modules.
متن کاملCOTORSION DIMENSIONS OVER GROUP RINGS
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.
متن کاملModel-theoretic aspects of Sigma-cotorsion modules
Let R be an associative ring with identity. It is shown that every Σ -cotorsion left R-module satisfies the descending chain condition on divisibility formulae. If R is countable, the descending chain condition on M implies that it must be Σ -cotorsion. It follows that, for countable R, the class of Σ -cotorsion modules is closed under elementary equivalence and pure submodules. The modules M t...
متن کاملOn n-Perfect Rings and Cotorsion Dimension
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.
متن کاملThe Cotorsion Dimension of Modules and Rings
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.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2005
ISSN: 0001-8708
DOI: 10.1016/j.aim.2004.01.006