On nilpotent elements of a free Jordan algebra (Q1068921)
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scientific article; zbMATH DE number 3931221
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On nilpotent elements of a free Jordan algebra |
scientific article; zbMATH DE number 3931221 |
Statements
On nilpotent elements of a free Jordan algebra (English)
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1985
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The author settles the following well-known question: does the free Jordan algebra contain nonzero nilpotent elements ? It is proved that the free countable generated Jordan algebra over a field F of characteristic greater than 7 contains nonzero nilpotent elements and nonzero absolute zero divisors. As a corollary it is proved that the free finitely generated Jordan algebra over F on more than 31 free generators contains a nonzero trivial ideal.
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prime characteristic greater seven
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free Jordan algebra
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nilpotent elements
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free countable generated Jordan algebra
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absolute zero divisors
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free finitely generated Jordan algebra
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free generators
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trivial ideal
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