Bi-ideals in Clifford ordered semigroup

Kalyan Hansda

Discussiones Mathematicae - General Algebra and Applications (2013)

  • Volume: 33, Issue: 1, page 73-84
  • ISSN: 1509-9415

Abstract

top
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.

How to cite

top

Kalyan Hansda. "Bi-ideals in Clifford ordered semigroup." Discussiones Mathematicae - General Algebra and Applications 33.1 (2013): 73-84. <http://eudml.org/doc/270274>.

@article{KalyanHansda2013,
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.},
author = {Kalyan Hansda},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Clifford (completely regular) ordered semigroup; ordered idempotents; bi-ideals; quasi-ideals; Clifford ordered semigroups; completely regular ordered semigroups},
language = {eng},
number = {1},
pages = {73-84},
title = {Bi-ideals in Clifford ordered semigroup},
url = {http://eudml.org/doc/270274},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Kalyan Hansda
TI - Bi-ideals in Clifford ordered semigroup
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2013
VL - 33
IS - 1
SP - 73
EP - 84
AB - 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.
LA - eng
KW - Clifford (completely regular) ordered semigroup; ordered idempotents; bi-ideals; quasi-ideals; Clifford ordered semigroups; completely regular ordered semigroups
UR - http://eudml.org/doc/270274
ER -

References

top
  1. [1] A.K. Bhuniya and K. Hansda, Complete semilattice of ordered semigroups, communicated. 
  2. [2] R.A. Good and D.R. Hughes, Associated groups for a semigroup, Bull. Amer. Math. Soc. 58 (1952) 624-625. 
  3. [3] U. Hebisch and H.J. Weinert, Semirings: Algebraic Theory and Applications in Computer Science, World Scientific, Singapore, 1998. Zbl0934.16046
  4. [4] J.M. Howie, Fundamentals of Semigroup Theory, Clarendon Press, Oxford, 1995. 
  5. [5] A. Iampan, On bi-ideals of semigroups, Lobachevskii J. Math. 29 (2) (2008) 68-72. doi: 10.1134/S1995080208020042 Zbl1165.20321
  6. [6] N. Kehayopulu, Note on Green's relation in ordered semigroup, Math. Japonica 36 (1991) 211-214. 
  7. [7] N. Kehayopulu, On completely regular poe-semigroups, Math. Japonica 37 (1992) 123-130. Zbl0745.06007
  8. [8] N. Kehayopulu, On regular duo ordered semigroups, Math. Japonica 37 (1992) 535-540. Zbl0760.06006
  9. [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. [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. [11] S. Lajos, On (m,n)-ideals of semigroups, Abstract of Second Hunger. Math. Congress I (1960) 42-44. 
  12. [12] S. Lajos, On the bi-ideals in Semigroups, Proc. Japan Acad. 45 (8) (1969) 710-712. doi: 10.3792/pja/1195520625 Zbl0199.33702
  13. [13] S. Lajos, Notes on semilattices of groups, Proc. Japan Acad. 46 (2) (1970) 151-152. doi: 10.3792/pja/1195520460 Zbl0205.02402
  14. [14] S. Lajos, A characterization of Cliffordian semigroups, Proc. Japan Acad. 52 (9) (1976) 496-497. doi: 10.3792/pja/1195518214 Zbl0374.20068
  15. [15] S. Lajos, Some characterization of regular duo semigroup, Proc. Japan Acad. 46 (10) (1970) 1099-1101. doi: 10.3792/pja/1195526501 Zbl0209.04901
  16. [16] S. Lee and S. Kang, Characterization of regular po-semigroup, Commu. Korean Math. Soc. 14 (4) (1999) 687-691. Zbl0969.06014
  17. [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. [18] O. Steinfeld, Quasi-ideals in rings and regular semigroups, Akademiai Ki-ado, Budapest (1958). doi: 10.1007/BF02572529 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.