Projective resolutions over Artin algebras with zero relations (Q801146)
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scientific article; zbMATH DE number 3877373
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Projective resolutions over Artin algebras with zero relations |
scientific article; zbMATH DE number 3877373 |
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Projective resolutions over Artin algebras with zero relations (English)
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1985
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One proves that gl.dim \(A\leq n+1\) for finite dimensional algebras over a field K whose ordinary quiver is a tree and a minimal set of relations has cardinality n. Using covering techniques one shows also that, for a finite dimensional zero relations K-algebra B with m minimal relations, \(gl.\dim B=\infty\) or \(gl.\dim B\leq m^ 2+2.\)
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global dimension
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projective cover
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universal cover
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finite dimensional algebras
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relations
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