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On bi-ideals of ordered Γ- semigroups – A Corrigendum

Year 2013, Volume: 42 Issue: 5, 559 - 567, 01.05.2013

Abstract

This is a Corrigendum of the paper in [1]. We keep the numbering given in [1] and we add our remarks and corrections. We give, among others, the correct definition of a strongly regular po-Γ-semigroup, and we correct the proof of 2.19 Lemma given in [1]. As one can see below, each of the papers in the References of the present paper contains its corresponding result in [1] and only such papers are cited in the References of this corrigendum and nothing more.

References

  • Hila, K., Pisha, E. On bi-ideals on ordered Γ-semigroups I, Hacet. J. Math. Stat. 40 (6), 793–804, 2011.
  • Kehayopulu, N. Note on Green’s relations in ordered semigroups, Math. Japon. 36 (2), 211–214, 1991.
  • Kehayopulu, N. On completely regular poe-semigroups, Math. Japon. 37 (1), 123–130, 1992. Kehayopulu, N. On completely regular ordered semigroups, Sci. Math. 1 (1), 27–32, 1998. Kehayopulu, N. On prime, weakly prime ideals in po-Γ-semigroups, Lobachevskii J. Math. 30 (4), 257–262, 2009.
  • Kehayopulu, N. On ordered Γ-semigroups, Sci. Math. Jpn. 71 (2), 179–185, 2010.
  • Kehayopulu, N. On regular duo po-Γ-semigroups, Math. Slovaca 61 (6), 871–884, 2011.
  • Kehayopulu, N., Ponizovskii, J. S., Tsingelis, M. Note on bi-ideals in ordered semigroups and in ordered groups, Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 265 (1999), Vopr. Teor. Predst. Algebr i Grupp. 6, 198–201, 327 (2000); translation in J. Math. Sci. (New York) 112, no. 4 (2002), 4353–4354.
  • Kehayopulu, N., Tsingelis, M. A characterization of strongly regular ordered semigroups, Math. Japon. 48 (2), 213–215, 1998.
  • Kehayopulu, N., Tsingelis, M. On left regular ordered semigroups, Southeast Asian Bull. Math. 25 (4), 609–615, 2002.
  • Kehayopulu, N., Tsingelis, M. Fuzzy bi-ideals in ordered semigroups, Inform. Sci. 171 (1–3), 13–28, 2005.
  • Sen, M. K., Saha, N. K. On Γ-semigroup I, Bull. Calcutta Math. Soc. 78, 180–186, 1986. Sen, M. K., Seth, A. On po-Γ-semigroups, Bull. Calcutta Math. Soc. 85 (5), 445–450, 1993. Zhu, Qingshun On characterizations of completely regular ordered semigroups, Southeast Asian Bull. Math. 29 (4), 827–834, 2005.
Year 2013, Volume: 42 Issue: 5, 559 - 567, 01.05.2013

Abstract

References

  • Hila, K., Pisha, E. On bi-ideals on ordered Γ-semigroups I, Hacet. J. Math. Stat. 40 (6), 793–804, 2011.
  • Kehayopulu, N. Note on Green’s relations in ordered semigroups, Math. Japon. 36 (2), 211–214, 1991.
  • Kehayopulu, N. On completely regular poe-semigroups, Math. Japon. 37 (1), 123–130, 1992. Kehayopulu, N. On completely regular ordered semigroups, Sci. Math. 1 (1), 27–32, 1998. Kehayopulu, N. On prime, weakly prime ideals in po-Γ-semigroups, Lobachevskii J. Math. 30 (4), 257–262, 2009.
  • Kehayopulu, N. On ordered Γ-semigroups, Sci. Math. Jpn. 71 (2), 179–185, 2010.
  • Kehayopulu, N. On regular duo po-Γ-semigroups, Math. Slovaca 61 (6), 871–884, 2011.
  • Kehayopulu, N., Ponizovskii, J. S., Tsingelis, M. Note on bi-ideals in ordered semigroups and in ordered groups, Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 265 (1999), Vopr. Teor. Predst. Algebr i Grupp. 6, 198–201, 327 (2000); translation in J. Math. Sci. (New York) 112, no. 4 (2002), 4353–4354.
  • Kehayopulu, N., Tsingelis, M. A characterization of strongly regular ordered semigroups, Math. Japon. 48 (2), 213–215, 1998.
  • Kehayopulu, N., Tsingelis, M. On left regular ordered semigroups, Southeast Asian Bull. Math. 25 (4), 609–615, 2002.
  • Kehayopulu, N., Tsingelis, M. Fuzzy bi-ideals in ordered semigroups, Inform. Sci. 171 (1–3), 13–28, 2005.
  • Sen, M. K., Saha, N. K. On Γ-semigroup I, Bull. Calcutta Math. Soc. 78, 180–186, 1986. Sen, M. K., Seth, A. On po-Γ-semigroups, Bull. Calcutta Math. Soc. 85 (5), 445–450, 1993. Zhu, Qingshun On characterizations of completely regular ordered semigroups, Southeast Asian Bull. Math. 29 (4), 827–834, 2005.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Niovi Kehayopulu This is me

Publication Date May 1, 2013
Published in Issue Year 2013 Volume: 42 Issue: 5

Cite

APA Kehayopulu, N. (2013). On bi-ideals of ordered Γ- semigroups – A Corrigendum. Hacettepe Journal of Mathematics and Statistics, 42(5), 559-567.
AMA Kehayopulu N. On bi-ideals of ordered Γ- semigroups – A Corrigendum. Hacettepe Journal of Mathematics and Statistics. May 2013;42(5):559-567.
Chicago Kehayopulu, Niovi. “On Bi-Ideals of Ordered Γ- Semigroups – A Corrigendum”. Hacettepe Journal of Mathematics and Statistics 42, no. 5 (May 2013): 559-67.
EndNote Kehayopulu N (May 1, 2013) On bi-ideals of ordered Γ- semigroups – A Corrigendum. Hacettepe Journal of Mathematics and Statistics 42 5 559–567.
IEEE N. Kehayopulu, “On bi-ideals of ordered Γ- semigroups – A Corrigendum”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 5, pp. 559–567, 2013.
ISNAD Kehayopulu, Niovi. “On Bi-Ideals of Ordered Γ- Semigroups – A Corrigendum”. Hacettepe Journal of Mathematics and Statistics 42/5 (May 2013), 559-567.
JAMA Kehayopulu N. On bi-ideals of ordered Γ- semigroups – A Corrigendum. Hacettepe Journal of Mathematics and Statistics. 2013;42:559–567.
MLA Kehayopulu, Niovi. “On Bi-Ideals of Ordered Γ- Semigroups – A Corrigendum”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 5, 2013, pp. 559-67.
Vancouver Kehayopulu N. On bi-ideals of ordered Γ- semigroups – A Corrigendum. Hacettepe Journal of Mathematics and Statistics. 2013;42(5):559-67.