A bounded below, noncontractible, acyclic complex of projective modules (Q6547997)
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scientific article; zbMATH DE number 7857901
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bounded below, noncontractible, acyclic complex of projective modules |
scientific article; zbMATH DE number 7857901 |
Statements
A bounded below, noncontractible, acyclic complex of projective modules (English)
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31 May 2024
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Bounded above acyclic complexes of projective objects and bounded below acyclic complexes of injective objects are contractible. On the other hand, there is an example of a doubly unbounded, acyclic, noncontractible complex of finitely generated projective-injective modules. The author is addressing the following questions posed by Shaul: Do there exist bounded below (resp. above), noncontractible, acyclic complexes of projective (resp. injective) modules? The aim of the paper is to construct examples of bounded below (resp. above), noncontractible, acyclic complexes of finitely generated projective (resp. injective) modules over some rings S. At the end, an example of a bounded below, noncontractible, acyclic complex of free modules with one generator, communicated to the author by A. Canonaco, is included.
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acyclic complex
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projective module
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injective module
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flat module
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coalgebra over a field
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comodule
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contramodule
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