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On a problem of Baayen and Kruyswijk

Published online by Cambridge University Press:  20 January 2009

D. A. Burgess
D. A. Burgess
Affiliation:
The University Nottingham
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We shall call a finite semigroup S arithmetical if there exists a positive integer N and a monomorphism μ of S into the multiplicative semigroup RN of the ring of residue classes of the integers modulo N. In 1965 P. C. Baayen and D. Kruyswijk [1] posed the problem' Is every finite commutative semigroup arithmetical? ' The purpose of this paper is to answer this question.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 2 , December 1968 , pp. 145 - 149
Copyright
Copyright © Edinburgh Mathematical Society 1968

References

REFERENCES

(1) Baayen, P. C. and Kruyswijk, D., A note on the multiplicative semigroup the residue classes modulo n, Math. Centrum Amsterdam Afd. Zuivere Wisk. ZW 1965–007.Google Scholar
(2) Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, vol.1, Math. Surveys of the American Math. Soc. 7 (Providence, R. I., 1961).Google Scholar