On Ternary Semigroups Containing -Ideals
Abstract
In this article, we give a definition of the -ideal in a ternary semigroup. We study some interesting properties of the -ideal and the relationship between the proper two-sided ideal and the -ideal. Finally, we show that if a two-sided ideal is a regular ternary subsemigroup of a regular ternary semigroup then every -ideal of is also a -ideal of Keywords : ternary semigroup ; regular ternary semigroup ; two-sided ideal ; -idealReferences
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). - -hyperideal theory in ordered -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.
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). - -hyperideal theory in ordered -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.
Downloads
Published
2023-01-04
Issue
Section
Research Article
