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Diassociative groupoids are not finitely based

Published online by Cambridge University Press:  09 April 2009

David M. Clark
David M. Clark
Affiliation:
Emory University Atlanta, GeorgiaU.S.A.
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In [2] Evans and Neumann raised the question of whether diassociativity in groupoids or loops is equivalent to a finite set of identities and in [3], Neumann still lists the problem as unsolved. It is the purpose of this paper to show that the answer to the question for groupoids is negative.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 1 , February 1970 , pp. 113 - 114
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Evans, Trevor, ‘The number of semigroup varieties’, Quart. J. Math. Oxford (2), 19 (1968), 335–336.Google Scholar
[2]Evans, Trevor and Neumann, B. H., ‘Varieties of groupoids and loops’, J. London Math. Soc. 28 (1953), 342–350.CrossRefGoogle Scholar
[3]Neumann, B. H., Special Topics in Algebra: Universal Algebra. Lecture notes prepared by Neumann, Peter M.. Courant Institute of Mathematical Sciences, New York University, 1962.Google Scholar