Partial orders in regular semigroups

• Srinivas, K. V. R. ^[2] ; Anasuya, Y. L. ^[1]
  1. [1] Andhra University

     Andhra University

     India

     
  2. [2] Regency institute of technology.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 29, Nº. 3, 2010, págs. 193-199
• Idioma: inglés
• DOI: 10.4067/S0716-09172010000300003
• Enlaces
  • Texto completo
• Resumen

  • First we have obtained equivalent conditions for a regular semigroup and is equivalent to N = N1 It is observed that every regular semigroup is weakly separative and C ⊆ S and on a completely regular semigroup S ⊆  N and S is partial order . It is also obtained that a band (S, .) is normal iff C = N . It is also observed that on a completely regular semigroup (S, .), C = S = N iff (S, .) is locally inverse semigroup and the restriction of C to E(S) is the usual partial order on E(S). Finally it is obtained that, if (S, .) is a normal band of groups then C = S = N .

• Referencias bibliográficas
  • Citas [1] Conrad, P. F., The hulls of semiprime rings, Bull. Austral. Math. Soc. 12, pp. 311314(1975).
  • [2] Burgess, W. D., Raphael, R., On Conrads partial order relation on semiprime rings and semigroups, Semigroup Forum 16, pp. 133140, (1978).
  • [3] Nambooripad, K. S. S., The natural partial order on a regular semigroup, Proc. Edinburgh Math. Soc. 23, pp. 249260, (1980).
  • [4] Drazin, M. P., A partial order in completely regular semigroups, J. Algebra 98, pp. 362374, (1986).
  • [5] Liu, Guo-Xin, Song, Guang-tian, Some partial orders on completely regular semigroups, J. Univ. Sci. and Tech. China 34, No. 5, pp. 524528,...
  • [6] Petrich, M., Reilly, N., Completely Regular Semigroups, Wiley Sons, New York, (1999).
  • [7] Petrich, M., Introduction to Semigroups, Charles E. Merrill Publ. Comp., Columbus, Ohio, (1973).
  • [8] Howie, J. M., Fundamentals of Semigroup Theory, Clarendon Press, Oxford (1995).
  • [9] Grillet, P. A., Semigroups. An Introduction to the Structure Theory, Pure and Applied Mathematics 193, Marcel Dekker, New York (1995).
  • [10] Ramana Murthy, P. V., Srinivas, K. V. R., Characterization of partial orders on regular semigroups, A. P. Akademi of sciences, Hyderabad,...