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Equationally complete varieties of generalized groups

Published online by Cambridge University Press:  17 April 2009

W.F. Page
W.F. Page
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, Florida, USA.
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Abstract

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In previous work, Page and Butson [Algebra Universalis 3 (1973), 112–126] characterized all equationally complete classes (atoms) of m–semigroups (universal algebras with one m–ary associative operation), and hence m–groups, in the commutative case. The further characterization of the non-commutative m-group atoms was thought to hinge upon a conjecture by Page [PhD thesis, University of Miami, 1973] that a weaker form of commutativity held true. In this paper that conjecture is proved and then used to study the special case m = 4. Two additional infinite sets of atoms are thereby determined, although it is not proved that these examples exhaust the remaining atoms for m = 4.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 1 , August 1975 , pp. 75 - 83
Copyright
Copyright © Australian Mathematical Society 1975

References

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