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Principal train algebras of rank 3 and dimensions≦5

Published online by Cambridge University Press:  20 January 2009

R. Costa
R. Costa
Affiliation:
Permanent Address Instituto de Matemática e Estatistica, Universidade de Sāo Paulo, Caixa Postal 20570− Ag. Iguatemi—CEP 01498, Sāo, Paulo, Brazil
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Abstract

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A commutative algebra A over the field F, endowed with a non-zero homorphism ω:A →F is principal train if it satisfies the identity xr+y1ω(x)xr−1 +… +yr−1ω(x)r−1x=0 where y1,…,yr−1 are fixed elements in F. We present in this paper, after the introduction of the concept of “type” of A, some results concerning the classification in the case r = 3. In particular we describe all these algebras of dimension≦5.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 1 , February 1990 , pp. 61 - 70
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

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