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A note on local polynomial functions on commutative semigroups

Part of: Semigroups Algebraic structures

Published online by Cambridge University Press:  09 April 2009

P. A. Grossman
P. A. Grossman
Affiliation:
Department of Mathematics Chisholm Institute of Technology(Caulfield Campus) Caulfield East, Victoria 3145, Australia
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Abstract

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Given a universal algebra A, one can define for each positive integer n the set of functions on A which can be “interpolated” at any n elements of A by a polynomial function on A. These sets form a chain with respect to inclusion. It is known for several varieties that many of these sets coincide for all algebras A in the variety. We show here that, in contrast with these results, the coincident sets in the chain can to a large extent be specified arbitrarily by suitably choosing A from the variety of commutative semigroups.

MSC classification

Secondary: 08A40: Operations, polynomials, primal algebras 20M14: Commutative semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 50 - 53
Copyright
Copyright © Australian Mathematical Society 1982

References

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