Cubic Ideals of TM-algebras

Main Article Content

Fatima M. Ghlaim
Fatema F. Kareem


For the generality of fuzzy ideals in TM-algebra, a cubic ideal in this algebra has been studied, such as cubic ideals and cubic T-ideals. Some properties of these ideals are investigated. Also, we show that the cubic T-ideal is a cubic ideal, but the converse is not generally valid. In addition, a cubic sub-algebra is defined, and new relations between the level subset and a cubic sub-algebra are discussed. After that, cubic ideals and cubic T-ideals under homomorphism are studied, and the image (pre-image) of cubic T-ideals is discussed. Finally, the Cartesian product of cubic ideals in Cartesian product TM-algebras is given. We proved that the product of two cubic ideals of the Cartesian product of two TM-algebras is also a cubic ideal.

Article Details

How to Cite
Cubic Ideals of TM-algebras. (2023). Ibn AL-Haitham Journal For Pure and Applied Sciences, 36(1), 367-379.
Author Biography

Fatima M. Ghlaim, Department of Mathematics , College of Education for Pure Sciences,Ibn Al –Haitham/ University of Baghdad



How to Cite

Cubic Ideals of TM-algebras. (2023). Ibn AL-Haitham Journal For Pure and Applied Sciences, 36(1), 367-379.

Publication Dates


Megalai, K.; Tamilarasi, A. Classification of TM-Algebra, Computer Aided Soft Computing Techniques for Imaging and Biomedical Applications. Special Issue 2010.

Ganeshkumar, T.; Chandramouleeswaran, M. t−DERIVATIONS ON TM-ALGEBRAS. International Journal of Pure and Applied Mathematics. 2013,85,1, 95-107.

Megalai, K. ; Tamilarasi, A. Fuzzy Subalgebras and Fuzzy T-ideals in TM-Algebras. Journal of Mathematics and Statistics. 2011, 7,2, 107-111.

Thomas, J.; Indhira, K.; Chandrasekaran, V. M. T-Normed Fuzzy TM-Subalgebra of TM-Algebras. International Journal of Computational Intelligence Systems. 2019,12,2, 706–712.

Ghlaim, F. M. ; Kareem, F. F. Interval valued fuzzy ideals of TM-algebra. Accepted in Journal of Interdisciplinary Mathematics.

Ganeshkumar, T. Generalized Derivation on TM –Algebras. International Journal of Algebra. 2013, 7, 6, 251 – 258.

Jun, Y. B. ; Kim, C. S. ; Kang, M. S. Cubic subalgebras and ideals of BCK/BCI-algebras. Far East Journal of Mathematical Sciences. 2010, 2, 44, 239–250.

Jun, Y. B. ; Kim, C. S. ; Yang, K.O. Cubic sets. Annals of Fuzzy Mathematics and Informatics. 2012, 1,4, 83–98.

Yaqoob, N.; Mostafa, S.M. ; Ansari, M.A. On cubic KU-ideals of KU-algebras.ISRN Algebra. 2013. Article ID935905, 10 pages.

Kareem, F. F. ; Hasan, O. A. Cubic ideals of semigroup in KU-algebra. J. Phys.: Conf. Ser. 1804. 2021, 012018.

Akram, M. ; Yaqoob, N.; Gulistan, M. cubic KU-subalgebras. Int. J. Pure Appl. Math. 2013,89 ,5, 659- 665.

Jun, Y. B. ; Kim, C. S. ; Kang ; Kang, J. G. Cubic q -ideals of BCI-algebras. Annals of Fuzzy Mathematics and Informatics. 2011, 1, 1, 25- 34.

Janaa, C.; Senapati, T. Cubic G-subalgebras of G-algebras. Annals of Pure and Applied Mathematics. 2015, 10,1, 105-115.