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On Ext-universal modules in Gödel's universe
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Lutz Strüngmann
Published/Copyright:
March 12, 2007
Abstract
Let R be an associative unital ring, T a left R-module and λ an infinite cardinal. We consider the class ⊥T of all left R-modules M satisfying ExtR1(M, T) = 0 and search for λ-universal objects in suitable subclasses ℭ of ⊥T. Here, an R-module U ∈ ℭ is λ-universal for T if |U| ≤ λ and every R-module M ∈ ℭ of cardinality less than or equal to λ embeds into U. We show that the existence of |T|-universal objects which are strong splitters implies the existence of λ-universal objects for sufficiently large λ if we assume (V = L). We then apply our results to module classes over small Dedekind domains to partially solve a generalized problem by Kulikov.
Received: 2005-09-27
Accepted: 2005-11-09
Published Online: 2007-03-12
Published in Print: 2007-03-20
© Walter de Gruyter
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Articles in the same Issue
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
Articles in the same Issue
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
