On identities of baric algebras and superalgebras (Q1375352)
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scientific article; zbMATH DE number 1104105
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On identities of baric algebras and superalgebras |
scientific article; zbMATH DE number 1104105 |
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On identities of baric algebras and superalgebras (English)
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25 March 1998
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Baric algebras are one type of genetic algebras. They arise in connection with a certain mathematical model in population genetics [see \textit{A. Wörz-Buzekros}, Algebras in genetics, Lecture Notes in Biomathematics 36, Springer-Verlag (1980; Zbl 0431.92017)]. The main results are the following two theorems. Theorem 1. Let \((A,\omega)\) be a Jordan-Bernstein or nuclear Bernstein algebra over a field of characteristic 0. Then the ideal \(T(A,\omega)\) has a finite set of generators. Theorem 2. Let \((A,\omega)\) be a Jordan or nuclear Bernstein algebra. Then \(T(A,\omega)\) is equal to the ideal of identities of the Grassmann envelope of a finitely generated baric superalgebra.
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baric algebras
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superalgebras
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identities
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nuclear Bernstein algebra
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0.8982688
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0.8890799
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