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'non-associative algebra'
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| Title of object: |
non-associative algebra |
| Canonical Name: |
NonAssociativeAlgebra |
| Type: |
Definition |
| Created on: |
2005-03-04 13:25:21 |
| Modified on: |
2006-05-27 00:41:49 |
| Classification: |
msc:17A01 |
| Defines: |
non-associative ring |
Revision comment (for changes between this and next version):
| Changes for correction #8321 ('spelling'). |
Preamble:
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Content:
A \emph{non-associative algebra} is an algebra in which the assumption of multiplicative associativity is dropped. From this definition, a non-associative algebra does not mean that the associativity fails. Rather, it enlarges the class of associative algebras, so that any associative algebra is a non-associative algebra.
In much of the literature concerning non-associative algebras, where the meaning of a ``non-associative algebra'' is clear, the word ``non-associative'' is dropped for simplicity and clarity.
Lie algebras and Jordan algebras are two famous examples of non-associative algebras that are not associative.
If we substitute the word ``algebra'' with ``ring'' in the above paragraphs, then we arrive at the defintion of a \emph{non-associative ring}. Alternatively, a non-associative ring is just a non-associative algebra over the integers.
\begin{thebibliography}{6}
\bibitem{rs} Richard D. Schafer, {\em An Introduction to Nonassociative Algebras}, Dover Publications, (1995).
\end{thebibliography} |
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