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Maximal Pre-Primal Clusters

Published online by Cambridge University Press:  20 November 2018

Jon Froemke
Jon Froemke*
Affiliation:
Oakland University, Rochester, Michigan
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A number of unsolved problems of primal algebra theory concern the existence of certain collections of dependent primal algebras. In [3] E. S. O'Keefe showed that any collection of pairwise non-isomorphic primal algebras of type {n} with n > 1 forms a primal cluster. Recently the author has discovered that if τ is any type containing at least two elements, one of which is > 1, then there are at least two non-isomorphic dependent primal algebras of type τ, except possibly in the case = {2, 0}; this result will appear later.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 4 , 01 August 1975 , pp. 746 - 751
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Gràtzer, G., Universal algebra (Princeton, N.J., Van Nostrand, 1968).Google Scholar
2. Jablonskii, S. V., Functional constructions in a k-valued logic (Russian), Trudy Mat. Inst. Steklov 51 (1958), 5–142.Google Scholar
3. O, E. S.'Keefe, On the independence of primal algebras, Math. Z. 73 (1960), 79–94.Google Scholar
4. Primal clusters of two-element algebras, Pac. J. Math. 11 (1961), 1505–1510.Google Scholar
5. Sioson, F. M., Some primal clusters, Math. Z. 75 (1960/61), 201–210.Google Scholar