Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-15T05:45:27.225Z Has data issue: false hasContentIssue false
  • English
  • Français

Naturally ordered bands

Published online by Cambridge University Press:  18 May 2009

J. M. Howie
J. M. Howie
Affiliation:
University of GlasgowGlasgow, W. 2.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1.Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math. 42 (1941), 1037–1049.CrossRefGoogle Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, American Mathematical Society Mathematical Surveys No. 7, Vol. 1 (Providence, R. I., 1961).Google Scholar
3.Fantham, P. H. H., On the classification of a certain type of semigroup, Proc. London Math. Soc. (3) 10 (1960), 409–427.CrossRefGoogle Scholar
4.Green, J. A. and Rees, D., On semigroups in which xr = x, Proc. Cambridge Philos. Soc. 48 (1952), 35–40.CrossRefGoogle Scholar
5.McLean, D., Idempotent semigroups, Amer. Math. Monthly 61 (1954), 110–113.CrossRefGoogle Scholar
6.Munn, W. D., Semigroups and their algebras, Thesis, Cambridge (1955).Google Scholar
7.Petrich, Mario, The structure of a class of semigroups which are unions of groups, Notices Amer. Math. Soc. 12 No. 1, Part 1 (1965), p. 102.Google Scholar