On the Schur multiplier of augmented algebras (Q1264285)
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scientific article; zbMATH DE number 1195648
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Schur multiplier of augmented algebras |
scientific article; zbMATH DE number 1195648 |
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On the Schur multiplier of augmented algebras (English)
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7 February 2000
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Let \(R\) be a finitely generated free associative algebra over a field \(k\), \(A=R/I\), \(I\) is not \(0\). If \(A\) is infinite-dimensional over \(k\), J. Lewin (1973) proved that \(R/I^2\) is not finitely presented. A stronger statement would be that the Schur multiplier of \(R/I^2\) is not finite-dimensional. This stronger statement is proved in the case that \(A\) is an augmented domain.
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finitely presented algebras
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finitely generated free associative algebras
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Schur multipliers
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augmented domains
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