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Naturally ordered bands

Published online by Cambridge University Press:  18 May 2009

J. M. Howie
J. M. Howie
Affiliation:
University of GlasgowGlasgow, W. 2.
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In the terminology of Clifford and Preston [2], a band B is a semigroup in which every element is idempotent. On such a semigroup there is a natural (partial) order relation defined by the rule

If the order relation ≧ is compatible with the multiplication in B, in the sense that e ≧ f and g ≧ h together imply that eg ≧ fh, we shall say that B is a naturally ordered band. The object of this note is to describe the structure of naturally ordered bands.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 8 , Issue 1 , January 1967 , pp. 55 - 58
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

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