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Fuzzy Derivations BCC-Ideals on BCC-Algebras

Received: 27 August 2015     Accepted: 9 September 2015     Published: 18 September 2015
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Abstract

In the theory of rings, the properties of derivations are important. In [15], 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.

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 5)
DOI 10.11648/j.pamj.20150405.14
Page(s) 225-232
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

BCC-Ideals, Fuzzy Left (Right)-Derivations, the Cartesian Product of Fuzzy Derivations

References
[1] 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.
[2] P. Bhattacharye and N. P. Mukheriee, Fuzzy relations and fuzzy group inform, sci, 36(1985), 267-282.
[3] W. A. Dudek, Y. B. Jun, Zoran Stojakovic, “On fuzzy ideals in BCC-algebras,” Fuzzy Sets and Systems 123 (2001) 251-258.
[4] W. A. Dudek .The number of subalgebras of finite BCC-algebras, Bull. Inst. Math. Acad. Sinica, 20 (1992), 129–136.
[5] W. A. Dudek., On proper BCC-algebras, Bull. Inst. Math. Acad. Sinica, 20 (1992), 137–150.
[6] W. A. Dudek. and Y. B Jun, , Fuzzy BCC-ideals in BCC-algebras, Math. Montisnigri, 10 (1999), 21–30.
[7] W. A. Dudek. and Y. B Jun and C. Z .Stojakovi_, On fuzzy ideals in BCCalgebras,Fuzzy Sets and Systems, 123 (2001), 251–258.
[8] W. A. Dudek, and X.H Zhang, On ideals and congruences in BCCalgebras, Czechoslovak Math. J., 48 (123) (1998), 21–29.
[9] A. S. A Hamza and N. O. Al-Shehri. 2006. Some results on derivations of BCI-algebras. Coden Jnsmac 46: 13-19.
[10] A. S. A Hamza and N. O. Al-Shehri. 2007. On left derivations of BCI-algebras. Soochow Journal of Mathematics 33(3): 435-444.
[11] Y. Huang, BCI-algebra, Science Press, Beijing, 2006.
[12] K. Is´eki, “On BCI-algebras,” Mathematics Seminar Notes, vol. 8, no. 1, pp. 125–130, 1980.
[13] K. Is´eki and S. Tanaka, “An introduction to the theory of BCKalgebras,” Mathematica Japonica, vol. 23, no. 1, pp. 1–26, 1978.
[14] K. Is´eki and S. Tanaka, “Ideal theory of BCK-algebras,” Mathematica Japonica, vol. 21, no. 4, pp. 351–366, 1976.
[15] Y. B. Jun, X. L. Xin. 2004. On derivations ofBCI-algebras. Information Sciences 159:167-176.
[16] Y. Komori, The class of BCC-algebras is not a variety, Math. Japonica, 29 (1984), 391–394.
[17] D. S. Malik and J. N. Mordeson, Fuzzy relation on rings and groups, Fuzzy Sets and Systems 43 (1991) 117-123.
[18] C. Prabpayak, Um Leerawat,On Derivations of BCC-algebras. Kasetsart J. (Nat. Sci.) 43: 398 - 401 (2009).
[19] A. Wro_nski, BCK-algebras do not form a variety, Math. Japonica, 28 (1983), 211–213.
[20] O. G. Xi, Fuzzy BCK-algebras, Math. Japon. 36 (1991), 935 942.
[21] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.
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  • APA Style

    Samy M. Mostafa, Mostafa A. Hassan. (2015). Fuzzy Derivations BCC-Ideals on BCC-Algebras. Pure and Applied Mathematics Journal, 4(5), 225-232. https://doi.org/10.11648/j.pamj.20150405.14

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    ACS Style

    Samy M. Mostafa; Mostafa A. Hassan. Fuzzy Derivations BCC-Ideals on BCC-Algebras. Pure Appl. Math. J. 2015, 4(5), 225-232. doi: 10.11648/j.pamj.20150405.14

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    AMA Style

    Samy M. Mostafa, Mostafa A. Hassan. Fuzzy Derivations BCC-Ideals on BCC-Algebras. Pure Appl Math J. 2015;4(5):225-232. doi: 10.11648/j.pamj.20150405.14

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  • @article{10.11648/j.pamj.20150405.14,
      author = {Samy M. Mostafa and Mostafa A. Hassan},
      title = {Fuzzy Derivations BCC-Ideals on BCC-Algebras},
      journal = {Pure and Applied Mathematics Journal},
      volume = {4},
      number = {5},
      pages = {225-232},
      doi = {10.11648/j.pamj.20150405.14},
      url = {https://doi.org/10.11648/j.pamj.20150405.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150405.14},
      abstract = {In the theory of rings, the properties of derivations are important. In [15], 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.},
     year = {2015}
    }
    

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    T1  - Fuzzy Derivations BCC-Ideals on BCC-Algebras
    AU  - Samy M. Mostafa
    AU  - Mostafa A. Hassan
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    JO  - Pure and Applied Mathematics Journal
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    AB  - In the theory of rings, the properties of derivations are important. In [15], 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.
    VL  - 4
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Author Information
  • Department of mathematics, Faculty of Education, Ain Shams University Roxy, Cairo, Egypt

  • Department of mathematics, Faculty of Education, Ain Shams University Roxy, Cairo, Egypt

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