Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-28T00:25:32.432Z Has data issue: false hasContentIssue false
  • English
  • Français

On right unipotent semigroups II

Published online by Cambridge University Press:  18 May 2009

P. S. Venkatesan
P. S. Venkatesan
Affiliation:
University of Ibadan, Ibadan, Nigeria
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.

We describe two congruences α and γ contained in ℒ on an arbitrary orthodox semigroup. Let S be a right unipotent semigroup. We show that (i) α is an inverse semigroup congruence and γ is the finest fundamental inverse semigroup congruence on S, (ii) S is a union of groups if and only if ℒ on S and (iii) S is a band of groups if and only if ℒ on S.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 1 , January 1978 , pp. 63 - 68
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Clifford, A. H., Bands of semigroups, Proc. Amer. Math. Soc. 5 (1954), 499–504.CrossRefGoogle Scholar
2.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys of the Amer. Math. Soc. 7 (Providence R.I., 1961 (Vol. 1) and 1967 (Vol. 2)).Google Scholar
3.Hall, T. E., On regular semigroups whose idempotents form a subsemigroup, Bull. Austral. Math. Soc. (1969), 195–208.CrossRefGoogle Scholar
4.Howie, J. M., The maximum idempotent-separating congruence on an inverse semigroup, Proc. Edinburgh Math. Soc. (2) 14 (1964), 71–79.CrossRefGoogle Scholar
5.Howie, J. M., Introduction to semigroup theory (Academic Press, 1976).Google Scholar
6.Lallement, G., Congruences et équivalences de Green sur un demi-groupe régulier, C.R. Acad. Sci. Paris Sér. A. 262 (1966), 613–616.Google Scholar
7.Meakin, J. C., Congruences on orthodox semigroups, J. Austral. Math. Soc. 12 (1971), 323–341.CrossRefGoogle Scholar
8.Munn, W. D., Fundamental inverse semigroups, Quart. J. Math. Oxford (2) 21 (1970), 157–170.CrossRefGoogle Scholar
9.Reilly, N. R. and Scheiblich, H. E., Congruences on regular semigroups, Pacific J. Math. 23 (1967), 349–360.CrossRefGoogle Scholar
10.Venkatesan, P. S., On decomposition of semigroups with zero, Math. Z. 92 (1966), 164–174.CrossRefGoogle Scholar
11.Venkatesan, P. S., Right (left) inverse semigroups, J. Algebra 31 (1974), 209–217.CrossRefGoogle Scholar
2.Venkatesan, P. S., On right unipotent semigroups, Pacific J. Math. 63 (1976), 555–561.CrossRefGoogle Scholar
13.Warne, R. J., L-unipotent semigroups, Nigerian J. Sci. (2) 5 (1972), 245–248.Google Scholar
14.Yamada, M., On a regular semigroup in which the idempotents form a band. Pacific J. Math. 33 (1970), 261–272.CrossRefGoogle Scholar