Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE ORDERED n-PRIME IDEALS IN ORDERED Γ-SEMIGROUPS

  • Siripitukdet, Manoj (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE NARESUAN UNIVERSITY) ;
  • Iampan, Aiyared (DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE NARESUAN UNIVERSITY)
  • Published : 2008.01.31
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Abstract

The motivation mainly comes from the conditions of the (ordered) ideals to be prime or semiprime that are of importance and interest in (ordered) semigroups and in (ordered) $\Gamma$-semigroups. In 1981, Sen [8] has introduced the concept of the $\Gamma$-semigroups. We can see that any semigroup can be considered as a $\Gamma$-semigroup. The concept of ordered ideal extensions in ordered $\Gamma$-semigroups was introduced in 2007 by Siripitukdet and Iampan [12]. Our purpose in this paper is to introduce the concepts of the ordered n-prime ideals and the ordered n-semiprime ideals in ordered $\Gamma$-semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered $\Gamma$-semigroups.

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References

  1. T. K. Dutta and N. C. Adhikari, On partially ordered $\Gamma$-semigroups, Southeast Asian Bulletin of Mathematics 28 (2004), 1021-1028
  2. A. Iampan and M. Siripitukdet, On minimal and maximal ordered left ideals in po-$\Gamma$-semigroups, Thai Journal of Mathematics 2 (2004), 275-282
  3. N. Kehayopulu, On weakly prime ideals of ordered semigroups, Mathematica Japonica 35 (1990), 1051-1056
  4. Y. I. Kwon and S. K. Lee, The weakly prime ideals of ordered-$\Gamma$-semigroups, Communications of the Korean Mathematical Society 13 (1998), 251-256
  5. Y. I. Kwon and S. K. Lee, The weakly semi-prime ideals of po-$\Gamma$-semigroups, Kangweon-Kyungki Mathematical Journal 5 (1997), 135-139
  6. S. K. Lee and Y. I. Kwon, A note on weakly prime ideals of ordered semigroups, Mathematica Japonica 50 (1999), 243-246
  7. N. K. Saha, On $\Gamma$-semigroup II, Bulletin of the Calcutta Mathematical Society 79 (1987), 331-335
  8. M. K. Sen, On $\Gamma$-semigroups, Proceedings of the International Conference on Algebra and it's Applications, Decker Publication, New York 301
  9. M. K. Sen and N. K. Saha, On $\Gamma$-semigroup I, Bulletin of the Calcutta Mathematical Society 78 (1986), 180-186
  10. M. K. Sen and N. K. Saha, Orthodox $\Gamma$-semigroups, International Journal of Mathematics and Mathematical Sciences 13 (1990), 527-534 https://doi.org/10.1155/S016117129000076X
  11. M. Siripitukdet and A. Iampan, On the least (ordered) semilattice congruences in ordered $\Gamma$-semigroups, Thai Journal of Mathematics 4 (2006), 403-415
  12. M. Siripitukdet and A. Iampan, On ordered ideal extensions in po-$\Gamma$-semigroups, Southeast Asian Bulletin of Mathematics, (to appear)