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Useful Theorems on Commutative Non-associative Algebras

Published online by Cambridge University Press:  20 January 2009

Nora Losey
Nora Losey
Affiliation:
University of Manitoba
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Recently J. M. Osborn has investigated the structure of a simple commutative non-associative algebra with unity element satisfying a polynomial identity, (4), (5) and (6). From his work it seems likely that if such an algebra is of degree three or more it is necessarily power-associative. In (4) he establishes a hierarchy of identities with the property that each identity is satisfied by an algebra satisfying no preceding identity. Following (5), (6),the next identity to consider is

where a, c and h are elements of the ground field.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 3 , June 1967 , pp. 203 - 208
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

REFERENCES

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