Nonexistence of a finite basis of identities of free 2-generator-solvable algebras of finite degree of freedom (Q1109860)
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scientific article; zbMATH DE number 4071137
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonexistence of a finite basis of identities of free 2-generator-solvable algebras of finite degree of freedom |
scientific article; zbMATH DE number 4071137 |
Statements
Nonexistence of a finite basis of identities of free 2-generator-solvable algebras of finite degree of freedom (English)
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1988
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The main result is that the identities of the free n-generator metabelian (nonassociative) algebra over an associative, commutative ring are infinitely based. More precisely, the identities \[ t_{n,k}=\sum_{\sigma \in S_{k+1}}(-1)^{\sigma}L(x_{\sigma_ 1})...L(x_{\sigma_ k})L(x_ k),...^{n-times},L(x_ k)L(x_{\sigma (k+1)}) \] are not consequences of polylinear identities of length \(\leq n+k\).
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variety of algebras
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metabelian algebras
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infinite basis of identities
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0.8295628428459167
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0.8003033995628357
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