Weakly Prime and Weakly Semiprime Left ideal in Ternary Semigroups

Authors

  • Pairote Yiarayong

Abstract

The purpose of this paper is to introduce the notion of a weakly prime ideals in ternary semigroups, we study left ideals, weakly prime and weakly semiprime ideals in ternary semigroups. Some characterizations of weakly semiprime and weakly prime ideals are obtained.

References

Bashir S., Shabir M., “Pure ideals in ternary semigroupsâ€, Quasigroups and Related Systems, vol. 17, (2009), 149 -160, 2009.

Changphas1 T., “m-systems and n-systems in ordered ternary semigroupsâ€, Gen. Math. Notes, vol. 7, no. 2, 59- 62, 2011.

Changphas T., “On maximal ideals in ternary semigroupsâ€, International Journal of Pure and Applied Mathematics, vol. 92, no. 1, 133-139, 2014.

Choosuwan P., Chinram R.,“A study on quasi-ideals in ternary semigroupsâ€, International Journal of Pure and Applied Mathematics, vol. 77, no. 5, 639-647, 2012.

Dixit V.N., Dewan S., “A note on quasi and bi-ideals in ternary semigroupâ€, Int. J. Math. Math. Sci., vol. 18, 501- 508, 1995.

Dixit V.N., Dewan S., “Minimal quasi-ideals in ternary semigroupâ€, Indian J. Pure Appl. Math., vol. 28, 625-632, 1997.

Dutta T.K.; Kar S.; Maity B.K., “On ideals in regular ternary semigroupsâ€, Discuss. Math. Gen. Algebra Appl., vol. 28, 147–159, 2008.

Lehmer D.H., “A ternary analogue of Abelian groupsâ€, Amer. J. Math., 329-338, 1932.

Los J., “On the extending of model Iâ€, Fundamenta Mathematicae, vol. 42, 38-54, 1955.

Iampan A., “Lateral ideals of ternary semigroupsâ€, Ukrainian Math. Bull., vol. 4, 525-534, 2007.

Jailoka1 P., Iampan A., “Minimality and maximality of ordered quasi-ideals in ordered ternary semigroupsâ€, Gen. Math. Notes, vol. 21, no. 2, 42-58, 2014.

Kar S., Maity B. K., “Congruences on ternary semigroupsâ€, Journal of the chungcheong mathematical society, vol. 20, no. 3, 191-201, 2007.

Kehayopulu N., “m-systems and n-systems in ordered ternary semigroupsâ€, Quasigroups and Relation Systems, vol. 11, 55-58, 2004.

Lekkoksung S., Lekkoksung N., “On intra-regular ordered ternary semigroupsâ€, Int. J. Math. Anal., vol. 6, 69-73, 2012.

Shabir M., Bano M., “Prime bi-ideals in ternary semigroupsâ€, Quasigroups and Related Systems, vol. 16 , 239- 256, 2008.

Sioson F.M., “Ideal theory in ternary semigroupsâ€, Math. Jpn., vol. 10, 63-84, 1965.

Sioson F.M., “Ideal theory in ternary semigroupsâ€, Math. Japon., vol. 10, 63-84, 1965.

Yaqoob N., Abdullah S., Rehman N., Naeem M., “Roughness and fuzziness in ordered ternary semigroupsâ€, World Applied Sciences Journal, vol. 17, no. 12, 1683-1693, 2012.

Downloads

Published

2015-08-17

How to Cite

Yiarayong, P. (2015). Weakly Prime and Weakly Semiprime Left ideal in Ternary Semigroups. Asian Journal of Applied Sciences, 3(4). Retrieved from https://ajouronline.com/index.php/AJAS/article/view/2425

Issue

Section

Articles

Most read articles by the same author(s)

1 2 > >>