Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-30T18:54:41.881Z Has data issue: false hasContentIssue false
  • English
  • Français

Semigroups of high rank II doubly noble semigroups

Published online by Cambridge University Press:  20 January 2009

Emilia Giraldes
Emilia Giraldes
Affiliation:
Departments de Matemática, Faculdade de Ciencias, Universidade de Lisboa, 1300 Lisboa, Portugal
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.

This paper is a sequel to [2]. By a semigroup of high rank we mean a semigroup such that for s1≠s2, 〈S\{s1,s2}〉⊂S (properly). Semigroups of high rank such that 〈S\{s}〉⊂S(royal semigroups) were classified in [2], where it was also shown that for a noble semigroup (i.e. a semigroup of high rank such that there exists a superfluous element z in S for which 〈S\{z}〉S) there exists eithere exactly one superfluous element or exactly two superfluous elements [2, Theorem 3.7].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 3 , October 1985 , pp. 409 - 417
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

1.Clifford, A. H., Semigroups admitting relative inverses, Ann. of Math. 42 (1941), 1037–1049.CrossRefGoogle Scholar
2.Giraldes, E. and Howie, John M., Semigroups of high rank, Proc. Edinburgh Math. Soc. 28 (1985), 13–34.CrossRefGoogle Scholar
3.Howie, J. M., An introduction to semigroup theory (Academic Press, London, 1976).Google Scholar
4.Mclean, D., Idempotent semigroups, American Math. Monthly 61 (1954), 110–113.CrossRefGoogle Scholar
5.Petrich, M., Lectures in semigroups (Akademie-Verlag, Berlin, 1977).CrossRefGoogle Scholar