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On varieties closed under the construction of power algebras

Published online by Cambridge University Press:  17 April 2009

A. Shafaat
A. Shafaat
Affiliation:
Département de Mathématique, Université Laval, Cité Universitaire, Québec, Canada.
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Abstract

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It is shown that if a variety V of (universal) algebras, defined by a set Σ of identities, is closed under the construction of power algebras then V can be defined by the subset Σ′ of Σ consisting of those identities ν = w of Σ such that every variable in ν = w occurs exactly once on both sides.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 2 , October 1974 , pp. 213 - 218
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Bleicher, M.N., Schneider, Hans and Wilson, R.L., “Permanence of identities on algebras”, Algebra Universalis 3 (1973), 72–93.CrossRefGoogle Scholar
[2]Cohn, P.M., Universal algebra (Harper and Row, New York, Evanston, London, 1965).Google Scholar
[3]Gautam, N.D., “The validity of equations of complex algebras”, Arch. Math. Logik Grundlagenforsch. 3 (1957), 117–124.CrossRefGoogle Scholar
[4]Whitney, Stephen, “Model classes of linear theories”, submitted.Google Scholar