Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T10:52:15.105Z Has data issue: false hasContentIssue false
  • English
  • Français

On Radicals of Green’s Relations in Ordered Semigroups

Published online by Cambridge University Press:  20 November 2018

Anjan Kumar Bhuniya  and
Kalyan Hansda
Anjan Kumar Bhuniya
Affiliation:
Department of Mathematics, Visva-Bharati University, Santiniketan, Bolpur - 731235, West Bengal, India. anjankbhuniya@gmail.com, kalyanh4@gmail.com
Kalyan Hansda
Affiliation:
Department of Mathematics, Visva-Bharati University, Santiniketan, Bolpur - 731235, West Bengal, India. anjankbhuniya@gmail.com, kalyanh4@gmail.com
Rights & Permissions [Opens in a new window]

Abstract

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 this paper, we give a new definition of radicals of Green’s relations in an ordered semigroup and characterize left regular (right regular), intra regular ordered semigroups by radicals of Green’s relations. We also characterize the ordered semigroups that are unions and complete semilattices of $\text{t}$-simple ordered semigroups.

Keywords

06F05radical of Green’s relationintra regular ordered semigroupleft regulart-simple ordered semigroup
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 2 , 01 June 2017 , pp. 246 - 252
Copyright
Copyright © Canadian Mathematical Society 2017

References

[1] Bhuniya, A. K. and Hansda, K., On completely regular and Clifford ordered semigroups. arxiv:1701.01282v1 Google Scholar
[2] Bogdanovic, S. and Ciric, M. A note on radicals of Green's relations. Pure Math Appl. 7(1996), 215–219. Google Scholar
[3] Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups. Vol. I. Mathematical Surveys, 7, American Mathematical Society, Providence, RI, 1961. Google Scholar
[4] Cao, Y., On weak commutativity of po-semigroups and their semilattice decompositions. Semigroup Forum 58(1999), 386–394. http://dx.doi.org/10.1007/BF03325436 Google Scholar
[5] Cao, Y., On completely regular poe-semigroups. Math. Japon. 37(1992), 123–130.Google Scholar
[6] Kehayopulu, N., Ideals and Green's relations in ordered semigroups. Int. J. Math. Math. Sci. (2006), Art. ID 61286. http://dx.doi.org/10.1155/IJMMS/2006/61286 Google Scholar
[7] Kehayopulu, N. and Tsingelis, M., On intra-regular ordered semigroups. Semigroup Forum 57(1998), 138–141. http://dx.doi.org/10.1007/PL00005962 Google Scholar
[8] Kehayopulu, N. and Tsingelis, M., On weakly commutative ordered semigroups. Semigroup Forum 56(1998), 32–35. http://dx.doi.org/10.1007/s00233-002-7002-6 Google Scholar
[9] Petrich, M., Lectures in semigroups. John Wiley & Sons, London-New York-Sydney, 1977. Google Scholar
[10] Pondelicek, B., A certain equivalence on a semigroup. Czechoslovak Math. J 21(96)(1971), 109–117. Google Scholar
[11] Sedlock, J. T., Green's relations on aperiodic semigroup. Czechoslovak Math. J 19(94)(1969), 318–322. Google Scholar
[12] Shevrin, L. N., Theory of epigroups. I. (Russian) Mat. Sbornik 185(1994), no. 8,129-160; translation in: Russian Acad. Sci. Sb. Math. 82(1995), 485–512. http://dx.doi.org/10.1070/SM1995v082n02ABEH003577 Google Scholar
[13] Zhu, Q.-S., On primary ideals and radical of ordered semigroups. Int. J. Pure Appl. Math. 55(2009), 335–342.Google Scholar