ArticleOriginal scientific text

Title

Bi-ideals in Clifford ordered semigroup

Authors 1

Affiliations

  1. Department of Mathematics, Visva Bharati Santiniketan, Bolpur - 731235 West Bengal, India

Abstract

In this paper we characterize both the Clifford and left Clifford ordered semigroups by their bi-ideals and quasi-ideals. Also we characterize principal bi-ideal generated by an ordered idempotent in a completely regular ordered semigroup.

Keywords

Clifford (completely regular) ordered semigroup, ordered idempotents, bi-ideals, quasi-ideals

Bibliography

  1. A.K. Bhuniya and K. Hansda, Complete semilattice of ordered semigroups, communicated.
  2. R.A. Good and D.R. Hughes, Associated groups for a semigroup, Bull. Amer. Math. Soc. 58 (1952) 624-625.
  3. U. Hebisch and H.J. Weinert, Semirings: Algebraic Theory and Applications in Computer Science, World Scientific, Singapore, 1998.
  4. J.M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford, 1995.
  5. A. Iampan, On bi-ideals of semigroups, Lobachevskii J. Math. 29 (2) (2008) 68-72. doi: 10.1134/S1995080208020042
  6. N. Kehayopulu, Note on Green's relation in ordered semigroup, Math. Japonica 36 (1991) 211-214.
  7. N. Kehayopulu, On completely regular poe-semigroups, Math. Japonica 37 (1992) 123-130.
  8. N. Kehayopulu, On regular duo ordered semigroups, Math. Japonica 37 (1992) 535-540.
  9. N. Kehayopulu, J.S. Ponizovskii and M. Tsingelis, Bi-ideals in ordered semigroups and ordered groups, J. Math. Sciences 112 (4) (2002). ISSN: 1573-8795
  10. N. Kehayopulu, Ideals and Green's relations in ordered semigroups, International Journal of Mathematics and Mathematical Sciences (2006), 1-8, Article ID 61286. doi: 10.1155/IJMMS/2006/61286
  11. S. Lajos, On (m,n)-ideals of semigroups, Abstract of Second Hunger. Math. Congress I (1960) 42-44.
  12. S. Lajos, On the bi-ideals in Semigroups, Proc. Japan Acad. 45 (8) (1969) 710-712. doi: 10.3792/pja/1195520625
  13. S. Lajos, Notes on semilattices of groups, Proc. Japan Acad. 46 (2) (1970) 151-152. doi: 10.3792/pja/1195520460
  14. S. Lajos, A characterization of Cliffordian semigroups, Proc. Japan Acad. 52 (9) (1976) 496-497. doi: 10.3792/pja/1195518214
  15. S. Lajos, Some characterization of regular duo semigroup, Proc. Japan Acad. 46 (10) (1970) 1099-1101. doi: 10.3792/pja/1195526501
  16. S. Lee and S. Kang, Characterization of regular po-semigroup, Commu. Korean Math. Soc. 14 (4) (1999) 687-691.
  17. M.M. Miccoli, Bi-ideals in regular semigroups and orthogroups, Acta. Math. Hung. 47 (1-2) (1986) 3-6. doi: 10.1007/BF01949118
  18. O. Steinfeld, Quasi-ideals in rings and regular semigroups, Akademiai Ki-ado, Budapest (1958). doi: 10.1007/BF02572529
Pages:
73-84
Main language of publication
English
Received
2012-01-15
Accepted
2013-03-08
Published
2013
Exact and natural sciences