Cubic BOI-ideal of BOI-algebra
Keywords:
BOI-algebra, BOI-subalgebra, BOI-ideal, cubic set, cubic BOI-ideal.
Abstract
In this paper, the notion of cubic BOI-ideal of BOI-algebra is introduced. Some characterization of cubic BOI-ideal of BOI-algebra is given. Several theorems are presented in this regard. The
homomorphic image and inverse image of cubic BOI-ideal are studied.
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References
[1] R. K. Bandaru. On BRK-algebras, Int. J. Math. Mathematical Sci. (2012), ID: 952654 12pp.
[2] O. R. El-Gendy, Anti Fuzzy BRK-ideal of BRK-algebra, British J. math, and Comp. Science, 10 (6) (2015) 1-9.
[3] O. R. El-Gendy, Cubic BRK-ideal of BRK-algebra, Annals of Fuzzy Mathematics and Informatics, 12(2) (2016), 245-253.
[4] O. R. El-Gendy, Fuzzy BRK-ideal of BRK-algebra, JP Journal of Algebra, Number Theory, and Applications, 36 (3) (2015), 231-240.
[5] O. R. El-Gendy, On BOI-algebra, Int. J. Math & Comp. App. Res. (IJMCAR), 9( 2) (2019), ID:IJMCARDEC20192,13-28.
[6] Q. P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11(2) (1983), 313-320.
[7] Y. Imai and K. IsΓ©ki, on axiom systems of propositional calculi, XIV. proc. Japan Academy, 42 (1966),19-22.
[8] C. Jana and M. Pal, On (ππΌ, ππΌ β¨ ππ½) -fuzzy soft BCI-algebras, Missouri Journal of Mathematical Sciences, 29(2) (2017),197-215.
[9] C. Jana, M. Pal, and A.B. Saied, (π, π β¨ π)-bipolar fuzzy BCK/BCI-algebras, Missouri Journal of Mathematical Sciences, 29(2) (2017), 139-160.
[10] C. Jana, T. Senapati, and M. Pal, (π, π β¨ π)-intuitionistic fuzzy BCI-subalgebras of a BCI-algebra, Journal of Intelligent & Fuzzy Systems 31 (1) 2016, 613-621.
[11] C. Jana, T. Senapati, Cubic G-subalgebras of G-algebra, Annals of Pure and Applied Mathematics, 10 (1) 2015, 105-115.
[12] Y. B. Jun, C. S. Kim and M. S. Kang, Cubic Sub algebras and ideals of BCK/BCI-algebras, Far East. J. Math. Sci. (FJMS), 44 (2010), 239-250.
[13] Y. B. Jun, C. S. Kim, and K. O. Yang βCubic setsβ, Annals of fuzzy mathematics and informatics, 4(1) 2012, 83-98.
[14] C. B. Kim, H. S. Kim, On BG-algebras, math. J. 36 (1992), 15-20.
[15] J. Neggers and H. S. Kim, on B-algebras, 54 (2002), 21-29
[16] J. Neggers, S. S. Ahn and H. S. Kim, On Q-algebras, Int. J. Math. Sci. 27 (12) (2001), 749-757.
[17] T. Senapati, C. Jana, M. Pal, and Y.B. Jun, Cubic intuitionistic q-ideals of BCI- algebras, Symmetry, 10(12) (2018), 752.
[18] A. Walendziak, On BF- algebras, Math. Slovaca, 57 (2) (2007), 119-128.
[19] L. A. Zadeh, Fuzzy sets, Inform. And Control, 8 (1965), 338-353.
[2] O. R. El-Gendy, Anti Fuzzy BRK-ideal of BRK-algebra, British J. math, and Comp. Science, 10 (6) (2015) 1-9.
[3] O. R. El-Gendy, Cubic BRK-ideal of BRK-algebra, Annals of Fuzzy Mathematics and Informatics, 12(2) (2016), 245-253.
[4] O. R. El-Gendy, Fuzzy BRK-ideal of BRK-algebra, JP Journal of Algebra, Number Theory, and Applications, 36 (3) (2015), 231-240.
[5] O. R. El-Gendy, On BOI-algebra, Int. J. Math & Comp. App. Res. (IJMCAR), 9( 2) (2019), ID:IJMCARDEC20192,13-28.
[6] Q. P. Hu and X. Li, On BCH-algebras, Math. Sem. Notes Kobe Univ. 11(2) (1983), 313-320.
[7] Y. Imai and K. IsΓ©ki, on axiom systems of propositional calculi, XIV. proc. Japan Academy, 42 (1966),19-22.
[8] C. Jana and M. Pal, On (ππΌ, ππΌ β¨ ππ½) -fuzzy soft BCI-algebras, Missouri Journal of Mathematical Sciences, 29(2) (2017),197-215.
[9] C. Jana, M. Pal, and A.B. Saied, (π, π β¨ π)-bipolar fuzzy BCK/BCI-algebras, Missouri Journal of Mathematical Sciences, 29(2) (2017), 139-160.
[10] C. Jana, T. Senapati, and M. Pal, (π, π β¨ π)-intuitionistic fuzzy BCI-subalgebras of a BCI-algebra, Journal of Intelligent & Fuzzy Systems 31 (1) 2016, 613-621.
[11] C. Jana, T. Senapati, Cubic G-subalgebras of G-algebra, Annals of Pure and Applied Mathematics, 10 (1) 2015, 105-115.
[12] Y. B. Jun, C. S. Kim and M. S. Kang, Cubic Sub algebras and ideals of BCK/BCI-algebras, Far East. J. Math. Sci. (FJMS), 44 (2010), 239-250.
[13] Y. B. Jun, C. S. Kim, and K. O. Yang βCubic setsβ, Annals of fuzzy mathematics and informatics, 4(1) 2012, 83-98.
[14] C. B. Kim, H. S. Kim, On BG-algebras, math. J. 36 (1992), 15-20.
[15] J. Neggers and H. S. Kim, on B-algebras, 54 (2002), 21-29
[16] J. Neggers, S. S. Ahn and H. S. Kim, On Q-algebras, Int. J. Math. Sci. 27 (12) (2001), 749-757.
[17] T. Senapati, C. Jana, M. Pal, and Y.B. Jun, Cubic intuitionistic q-ideals of BCI- algebras, Symmetry, 10(12) (2018), 752.
[18] A. Walendziak, On BF- algebras, Math. Slovaca, 57 (2) (2007), 119-128.
[19] L. A. Zadeh, Fuzzy sets, Inform. And Control, 8 (1965), 338-353.
Published
2019-12-10
How to Cite
El-Gendy, O. R. (2019). Cubic BOI-ideal of BOI-algebra. Journal of Progressive Research in Mathematics, 15(4), 2781-2792. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1810
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