منابع مشابه
Relative 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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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.
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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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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...
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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,...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2012
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm217-3-2