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On some Schreier varieties of universal algebras

To Bernhard hermann Neumann on his 60th birthday

Published online by Cambridge University Press:  09 April 2009

Stephen Meskin
Stephen Meskin
Affiliation:
The Australian National University Canberra
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Let ω =(ω1) Where ω1 is a set of non-empty sets (called operations) and ω0 is a set of elements (called constants) none of which is a function whose domain belongs to ω1. An ω-ALGEBRA is a set C and a function e (the effect) from the disjoint union of ω0 and ω∈ω1Cω to C, where Cω is the set of all functions from ω to C. Let P be a set of groups Pω of permutations on ω, one group fro each ω∈ω1. A Ρ-ω-ALGEBRA is an ω-algebra such that (ρf)e = (f)e, for all ω ∈ ω1, ρ ∈ Ρω and f ∈ Cω.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 3-4 , November 1969 , pp. 442 - 444
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Cohn, P. M., Universal Algebra, (Harper and Row, New York, 1966).Google Scholar
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[3]Lewin, J., ‘On Schreier varieties of linear algebras’ Trans. Amer. Math. Soc. 132 (1968), 553–562.CrossRefGoogle Scholar
[4]Neumann, B. H., Universal Algebra (Notes from New York University, 1962).Google Scholar
[5]Pierce, R. S., Introduction to the Theory of Abstract Algebras, (Holt, Renchart and Winston, New York, 1968).Google Scholar