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On Extending Semigroup Characters

Published online by Cambridge University Press:  20 January 2009

Ronald Fulp
Ronald Fulp
Affiliation:
University of Houston
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The principal result of this paper is a characterisation of those commutative semigroups S which have the property that each character of each subsemigroup of S can be extended to a character of S. This work was partially inspired by the discovery that Theorem 5.65 of (1) is incorrect; it is related to that of Hill,who has obtained a different solution of the problem (2). Warne and Williams proved in (4) that any bounded character defined on an inverse subsemigroup of an inverse semigroup can be extended to the semigroup.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 3 , June 1967 , pp. 199 - 202
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

REFERENCES

(1) Clifford, A. H. and Preston, G. B., Algebraic theory of semigroups, Amer. Math. Soc. Math. Sur. 7 (1961).Google Scholar
(2) Hill, Paul, Characters of commutative semigroups, Journal of Algebra.Google Scholar
(3) Ross, K. A., Extending characters on semigroups, Proc. Amer. Math. Soc. 12 (1961).Google Scholar
(4) Warne, R. J. and Williams, L. K., Characters on inverse semigroups, Czech. Math. Jour. 11 (1961).Google Scholar