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Infinite independent systems of identities of an associative algebra over an infinite field of characteristic two. - MaRDI portal

Infinite independent systems of identities of an associative algebra over an infinite field of characteristic two. (Q1889574)

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scientific article; zbMATH DE number 2121071
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Infinite independent systems of identities of an associative algebra over an infinite field of characteristic two.
scientific article; zbMATH DE number 2121071

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    Infinite independent systems of identities of an associative algebra over an infinite field of characteristic two. (English)
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    2 December 2004
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    The paper under review gives constructions of infinite systems of identities in the free associative algebra over an infinite field of characteristic 2. This means that there exist T-ideals that have no finite systems of generators (as T-ideals). As a consequence, such systems of identities are obtained in the case of special Jordan algebras. We note that in the last several years there have been quite a lot of such examples, see, e.g., \textit{A. Ya. Belov} [Sb. Math. 191, No. 3, 329--340 (2000); translation from Mat. Sb. 191, No. 3, 13--24 (2000; Zbl 0960.16029)], and its bibliography. We only note that the paper under review was submitted in March 29, 1999.
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    varieties of algebras
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    nonfinitely based varieties
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    word problem
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    special Jordan algebras
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    independent systems of identities
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    Specht problem
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    T-ideals
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