On Trio Ternary 𝚪-Semigroups

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    In this paper the terms trio L-trio TΓ-ideal, La-trio TΓ-ideal, R-trio TΓ- ideal and trio TΓ- ideal of a TΓ-semi group are introduced and some examples are given. It is proved that (1) a TΓ-semi group T is a trio TΓ-semi group if and only if xΓTΓT = TΓTΓx = TΓxΓT  for all x ∈ T, (2) Every trio TΓ-semi group is a duo TΓ-semi group, (3) Every commutative TΓ-semi group is a trio TΓ-semi group (4) Every quasi commutative TΓ-semi group is a trio TΓ-semi group. 


  • Keywords


    duo TΓ-semi group, idempotent, prime trio TΓ-ideal, semi primary TΓ-semi group trio TΓ-semi group.

  • References


      [1] A. Gangadhara Rao, A. Anjaneyulu and D. Madhusudhana Rao, Prime Γ-ideals in Duo Γ-semigroups-International eJournal of Mathematics and Engineering 174 (2012) 1642-1653.

      [2] A. Gangadhara Rao, A. Anjaneyulu and D. Madhusudhana Rao, Duo Chained Γ-semigroups –International Journal of Mathematical Science, Technology and Humanities 50 (2012) 520-533.

      [3] A. Gangadhara Rao, A. Anjaneyulu and D. Madhusudhana Rao, Duo Noetheria Γ-semigroups, International eJournal of Mathematics and Engineering 178 (2012) 1688-1704.

      [4] K. Padmathi, M. Ramesh and D.Madhusudhana Rao, On Regular Duo Ternary Semigroups–International Journal of Multidisciplinary Educational Research, Volume 2, Issue 7(3), June 2013, pp: 78-87.

      [5] G. Srinivasa Rao and D. Madhusudhana Rao, Special Elements in Ternary Semirings-International Journal of Engineering Research and Applications, Vol 4, Issue 11, Version 5, November 2014.

      [6] G. Srinivasa Rao and D. Madhusudhana Rao, Structure of Certain Ideals in Ternary SemiringsInternational Journal of Innovative Science and Modern Engineering(IJISME), Volume-3, Issue-2, January 2015.

      [7] M. sajaniLavanya , D. Madhusudhana Rao and V. Syam Julius Rajendra and On Lateral Ternary Γ-Ideals of Ternary Γ-Semirings - American International Journal of Research in Science, Technology,Engineering &Mathematics(AIJRSTEM), 12(1), September-November, 2015, pp: 11-14.

      [8] M. Sajani Lavanya, D. Madhusudhana rao and P. Panduranga Rao, On Simple ternary 𝚪-Semiring, Vol.7-Issue 2(Part-5)February-2017, International Journal of Engineering Research and Applications(IJEERA), pp: 01-06.

      [9] Y, Sarala, A. Anjaneyulu and D. Madhusudhana Rao, Ideals in Ternary Semigroups- International eJournal of Mathematics and Engineering 203(2013) 1950-1968.

      [10] D. Madhusudhana Rao and M. Vasanths-Properties of Prime Ternary Γ-radicals in Ternary Γ-Semigroups - Global Journal of pure and Applied Mathematics, Volume 11, Issue 6 (2015), pp: 4255-4271.


 

View

Download

Article ID: 18287
 
DOI: 10.14419/ijet.v7i3.31.18287




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.