On Ternary Semigroups Containing CT -Ideals

Wichayaporn   Jantanan; Thongsa   Butngam; Natee  Raikham

Authors

Wichayaporn Jantanan Department of Mathematics, Faculty of Science, Buriram Rajabhat University
Thongsa Butngam Department of Statistics and Information Science, Faculty of Science, Buriram Rajabhat University
Natee Raikham Department of Mathematics, Faculty of Science, Buriram Rajabhat University

Keywords:

ternary semigroup, regular ternary semigroup , two-sided ideal , CT-ideal

Abstract

In this article, we give a definition of the C T -ideal in a ternary semigroup. We study some interesting properties of the C T-ideal and the relationship between the proper two-sided ideal and the C T-ideal. Finally, we show that if a two-sided ideal A is a regular ternary subsemigroup of a regular ternary semigroup S then every C T-ideal of A is also a C T -ideal of

References

Ali, M. F., & Khan, N. M. (2023). Characterization of ordered semihypergroups by covered hyperideals. Kragujevac Journal of Mathematics, 47(3), 417-429.

Bashir, S., & Shabir, M. (2009). Pure two-sided ideals in ternary semigroups. Quasigroups and Related Systems, 17(2), 149-160.

Changphas, T., & Summaprab, P. (2016). On ordered semigroups containing covered two-sided ideals. Communications in Algebra, 44(9), 4104-4113.

Dixit, V. N., & Dewan, S. (1995). A note on quasi and bi-ideals in ternary semigroups. International Journal of Mathematics and Mathematical Sciences, 18(3), 501-508.

Fabrici, I., (1984). Semigroups containing covered two-sided ideals. Mathematica Slovaca, 34(3), 355-363.

Kar, S., Roy, A., & Dutta, I. (2020). On regularities in po-ternary semigroups. Quasigroups and Related Systems, 28(1), 149-158.

Lehmer, D. H. (1932). A ternary analogue of abelian groups. American Journal of Mathematics, 54(2), 329-338.

Los, J. (1955). On the extending of models I. Fundamenta Mathematicae, 42(1), 38-54.

Omidi, S., & Davvaz, B. (2017). C-T -hyperideal theory in ordered T -semihypergroups. Journal of Mathematical and Fundamental Sciences, 49(2), 181-192.

Shabir, M., & Bano, M. (2008). Prime bi-ideals in ternary semigroup. Quasigroups and Related Systems, 16(2), 239-256.

Sioson, F.M. (1965). Ideal theory in ternary semigroups. Mathematica Japonica, 10, 63–84.

Thongkam, B., & Changphas, T. (2015). On two-sided bases of ternary semigroups. Quasigroups and Related Systems, 23(2), 319-324.