Identities of nearly triangular matrices (Q2784542)
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scientific article; zbMATH DE number 1732465
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Identities of nearly triangular matrices |
scientific article; zbMATH DE number 1732465 |
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Identities of nearly triangular matrices (English)
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2 June 2002
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block-triangular matrices
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codimension growth
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bases of identities
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polynomial identities
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ideals of identities
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The author studies identical relations of some algebras that are close to triangular matrices. The ideal of polynomial identities is described for block-triangular matrices over an infinite field, such that all matrices in this algebra have a fixed block structure and vanishing blocks are admitted. Then the ideal of identities is the product of the ideals of identities for the blocks, where to a vanishing block corresponds the ideal generated by one variable. This result is applied to some algebras of upper-triangular matrices. In case of characteristic zero, the asymptotic behaviour of the sequence of codimensions is found.
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