Pure and Applied Mathematics Journal
Volume 4, Issue 5, October 2015, Pages: 225-232
Received: Aug. 27, 2015;
Accepted: Sep. 9, 2015;
Published: Sep. 18, 2015
Views 4441 Downloads 198
Samy M. Mostafa, Department of mathematics, Faculty of Education, Ain Shams University Roxy, Cairo, Egypt
Mostafa A. Hassan, Department of mathematics, Faculty of Education, Ain Shams University Roxy, Cairo, Egypt
In the theory of rings, the properties of derivations are important. In , Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCC-ideals in BCC-algebras is introduced and then investigate their basic properties. In connection with the notion of homomorphism, the authors study how the image and the pre-image of fuzzy left (right) derivations BCC-ideals under homomorphism of BCC-algebras become fuzzy left (right) derivations BCC-ideals. Furthermore, the Cartesian product of fuzzy left (right) derivations BCC-ideals in Cartesian product of BCC-algebras is introduced and investigated some related properties.
Samy M. Mostafa,
Mostafa A. Hassan,
Fuzzy Derivations BCC-Ideals on BCC-Algebras, Pure and Applied Mathematics Journal.
Vol. 4, No. 5,
2015, pp. 225-232.
S. M. Bawazeer, N. O. Alshehri, and Rawia Saleh Babusail, “Generalized Derivations of BCC-Algebras,” International Journal of Mathematics and Mathematical Sciences, volume 2013, Article ID 451212, 4 pages.
P. Bhattacharye and N. P. Mukheriee, Fuzzy relations and fuzzy group inform, sci, 36(1985), 267-282.
W. A. Dudek, Y. B. Jun, Zoran Stojakovic, “On fuzzy ideals in BCC-algebras,” Fuzzy Sets and Systems 123 (2001) 251-258.
W. A. Dudek .The number of subalgebras of finite BCC-algebras, Bull. Inst. Math. Acad. Sinica, 20 (1992), 129–136.
W. A. Dudek., On proper BCC-algebras, Bull. Inst. Math. Acad. Sinica, 20 (1992), 137–150.
W. A. Dudek. and Y. B Jun, , Fuzzy BCC-ideals in BCC-algebras, Math. Montisnigri, 10 (1999), 21–30.
W. A. Dudek. and Y. B Jun and C. Z .Stojakovi_, On fuzzy ideals in BCCalgebras,Fuzzy Sets and Systems, 123 (2001), 251–258.
W. A. Dudek, and X.H Zhang, On ideals and congruences in BCCalgebras, Czechoslovak Math. J., 48 (123) (1998), 21–29.
A. S. A Hamza and N. O. Al-Shehri. 2006. Some results on derivations of BCI-algebras. Coden Jnsmac 46: 13-19.
A. S. A Hamza and N. O. Al-Shehri. 2007. On left derivations of BCI-algebras. Soochow Journal of Mathematics 33(3): 435-444.
Y. Huang, BCI-algebra, Science Press, Beijing, 2006.
K. Is´eki, “On BCI-algebras,” Mathematics Seminar Notes, vol. 8, no. 1, pp. 125–130, 1980.
K. Is´eki and S. Tanaka, “An introduction to the theory of BCKalgebras,” Mathematica Japonica, vol. 23, no. 1, pp. 1–26, 1978.
K. Is´eki and S. Tanaka, “Ideal theory of BCK-algebras,” Mathematica Japonica, vol. 21, no. 4, pp. 351–366, 1976.
Y. B. Jun, X. L. Xin. 2004. On derivations ofBCI-algebras. Information Sciences 159:167-176.
Y. Komori, The class of BCC-algebras is not a variety, Math. Japonica, 29 (1984), 391–394.
D. S. Malik and J. N. Mordeson, Fuzzy relation on rings and groups, Fuzzy Sets and Systems 43 (1991) 117-123.
C. Prabpayak, Um Leerawat,On Derivations of BCC-algebras. Kasetsart J. (Nat. Sci.) 43: 398 - 401 (2009).
A. Wro_nski, BCK-algebras do not form a variety, Math. Japonica, 28 (1983), 211–213.
O. G. Xi, Fuzzy BCK-algebras, Math. Japon. 36 (1991), 935 942.
L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.