Accessible subcategories of modules and pathological objects
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Abstract
Let λ be an infinite regular cardinal. It is proved, under the assumption of the Generalized Continuum Hypothesis, that any λ-accessible and λ-accessibly embedded subcategory 𝒦 of a category of modules closed under direct sums gives rise to non-trivial κ-separable modules, for arbitrarily large regular cardinals κ ≥ λ, when some modules of 𝒦 are not direct sum of λ-presentable modules (namely, those modules which are totally ordered λ-directed colimits of λ-presentable modules). In particular, it is shown that any ring R that is not left pure-semisimple has non-trivial λ-separable left modules for arbitrarily large regular cardinals λ. These results extend previous constructions by Corner, Griffith, Hill, Eklof, Shelah and Huisgen-Zimmermann. We point up that κ-separable modules satisfy certain generalized Mittag-Leffler conditions.
© de Gruyter 2010
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- Brill-Noether theory for moduli spaces of sheaves on algebraic varieties
- Homotopy type of mapping spaces and existence of geometric exponents
- Extension theorems for spheres in the finite field setting
- Accessible subcategories of modules and pathological objects
- Characteristic cohomotopy classes for families of 4-manifolds
- Generators of simple Lie algebras II
- L1-determined ideals in group algebras of exponential Lie groups
- Simple mass formulas on Shimura varieties of PEL-type
- Uniqueness for elliptic operators on with unbounded coefficients
- Homogeneous principal bundles and stability
Articles in the same Issue
- Brill-Noether theory for moduli spaces of sheaves on algebraic varieties
- Homotopy type of mapping spaces and existence of geometric exponents
- Extension theorems for spheres in the finite field setting
- Accessible subcategories of modules and pathological objects
- Characteristic cohomotopy classes for families of 4-manifolds
- Generators of simple Lie algebras II
- L1-determined ideals in group algebras of exponential Lie groups
- Simple mass formulas on Shimura varieties of PEL-type
- Uniqueness for elliptic operators on with unbounded coefficients
- Homogeneous principal bundles and stability
