Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-15T06:49:04.090Z Has data issue: false hasContentIssue false
  • English
  • Français

The Structure of Normal Inverse Semigroups

Published online by Cambridge University Press:  18 May 2009

G. B. Preston
G. B. Preston
Affiliation:
Royal Military College of Science, Shrivenham
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 a recent paper [1] we showed that there is a (1,) -correspondence between the homomorphisms of an inverse semigroup S and its normal subsemigroups. The normal subsemigroup of S corresponding to and determining the homomorphism μ of S is the inverse image under μ of the set of idempotents of Sμ and is called the kernel of the homomorphism μ. The inverse image of each idempotent of Sμ is itself an inverse semigroup [1], and each such inverse semigroup is said to be a component of the normal subsemigroup determined by μ.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 1 , December 1956 , pp. 1 - 9
Copyright
Copyright © Glasgow Mathematical Journal Trust 1956

References

REFERENCES

1.Preston, G. B., Inverse semi-groups, London Math. Soc., 29 (1954), 396–403.CrossRefGoogle Scholar
2.Clifford, A. H., Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499–504.CrossRefGoogle Scholar
3.Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math., 42 (1941), 1037–1049.CrossRefGoogle Scholar
4.Liber, A. E., K teorii obobščennyh grupp, Dokl. Akad. Nauk. SSSR, 97 (1954), 25–28.Google Scholar
5.Croisot, R., Demi-groupes inversifs et demi-groupes réunions de demi-groupes simples, Ann. de L'école Nortn., (3) 70 (1953), 361–379.CrossRefGoogle Scholar
6.Munn, W. D. and Penrose, R., A note on inverse semigroups, Proc. Cambridge Phil. Soc. 51 (1955), 396–399.CrossRefGoogle Scholar
7.Vagner, V. V., Obobščennye gruppy, Dokl. Akad. Nauk. SSSR, 84 (1952), 1119–1122.Google Scholar
8.Clifford, A. H., Extensions of semigroups, Trans. Amer. Math. Soc. 68 (1950), 165–173.CrossRefGoogle Scholar