Modules of infinite projective dimension over algebras whose idempotent ideals are projective (Q1375754)
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scientific article; zbMATH DE number 1102895
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Modules of infinite projective dimension over algebras whose idempotent ideals are projective |
scientific article; zbMATH DE number 1102895 |
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Modules of infinite projective dimension over algebras whose idempotent ideals are projective (English)
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23 April 1998
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The following result is proved: Let \(A\) be a finite dimensional algebra over an algebraically closed field. Suppose that each idempotent ideal is a projective left \(A\)-module. If the algebra \(A\) is representation-infinite and not hereditary, then \(A\) has a loop in its quiver and there exist infinitely many non-isomorphic indecomposable \(A\)-modules of infinite projective dimension.
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idempotent ideals
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projective dimensions
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finite dimensional algebras
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projective left modules
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representation infinite algebras
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indecomposable modules
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quivers
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