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flexible algebra
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(Definition)
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A non-associative algebra is flexible if
for all , where is the associator on . In other words, we have
for all . Any associative algebra is clearly flexible. Furthermore, any alternative algebra with characteristic is flexible.
Given an element in a flexible algebra , define the left power of iteratively as follows:
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Similarly, we can define the right power of as:
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.
Then, we can show that
for all positive integers . As a result, in a flexible algebra, one can define the (multiplicative) power of an element as unambiguously.
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"flexible algebra" is owned by CWoo.
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Cross-references: power, multiplicative, integers, positive, characteristic, alternative algebra, algebra, associative, associator, non-associative algebra
There are 11 references to this entry.
This is version 8 of flexible algebra, born on 2004-10-10, modified 2008-10-07.
Object id is 6351, canonical name is FlexibleAlgebra.
Accessed 2456 times total.
Classification:
| AMS MSC: | 17A20 (Nonassociative rings and algebras :: General nonassociative rings :: Flexible algebras) |
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Pending Errata and Addenda
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