Fuzzy Derivations BCC-Ideals on BCC-Algebras

Samy M. Mostafa; Mostafa A. Hassan

doi:doi:10.11648/j.pamj.20150405.14

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Fuzzy Derivations BCC-Ideals on BCC-Algebras

Samy M. Mostafa, Mostafa A. Hassan

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 5)

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

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[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.
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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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TY  - JOUR
T1  - Fuzzy Derivations BCC-Ideals on BCC-Algebras
AU  - Samy M. Mostafa
AU  - Mostafa A. Hassan
Y1  - 2015/09/18
PY  - 2015
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JF  - Pure and Applied Mathematics Journal
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PB  - Science Publishing Group
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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
IS  - 5
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Author Information

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Fuzzy Derivations BCC-Ideals on BCC-Algebras
AU  - Samy M. Mostafa
AU  - Mostafa A. Hassan
Y1  - 2015/09/18
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150405.14
DO  - 10.11648/j.pamj.20150405.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 225
EP  - 232
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150405.14
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
IS  - 5
ER  -

Copy | Download