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Generalization of ([e],[e]∨[c])-Ideals of BE-algebras

Year 2015, Volume: 3 Issue: 1, 1 - 11, 22.12.2014

Saleem Abdullah Ahmed Fawad Ali Muhammad S. Kamran Muhammad Aslam

Abstract

In this paper, using N-structure, the notion of an N-ideal in a BE-algebra is introduced. To obtain a more general form ofan N-ideal, a point N-structure which is (k-conditionally) employed in an N-structure is proposed. Using these notions, the conceptof an ([e], [e]∨ [ck])-ideal is introduced and related properties are investigated. The notion ([e], [e]∨ [ck])-ideal is a generalization of([e], [e]∨ [c])-ideal. We derive some characterizations of ([e],[e] ∨ [ck])-ideals of BE-algebras

Keywords

BE-algebra (Transitive self distributive) BE-algebra Ideal N-ideal ([e] [e]∨ [ck])-ideal

References

  • Ahn, S.S., Kim, Y.H., Ko, J.M, Filters in commutative BE-algebras. Commun. Korean Math. Soc., 27, (2012)(2), 233–242.
  • Y. H. Yon, S. M. Lee and K. H. Kim, On congruences and BE-relations in BE-Algebras, Int. Math. Forum, 5, 2010, 46, 2263-2270.
  • Kim, H.S., and Y.H. Kim, On BE-algebras, Scientiae Mathematicae Japonicae, 66, 2007, 1, 113-117.
  • H. S. Kim and K. J. Lee, Extended upper sets in BE-algebras, Bull. Malays. Math. Sci. Soc. (2) 34(3) (2011), 511–520.
  • Rezaei, A., and A. Borumand Saeid, Some results in BE-algebras, Analele Universitatii Oradea Fasc. Matematica, Tom XIX, 1 2012, 33-44.
  • K. S. So, and S. S. Ahn, On ideals and upper sets in BE-algebras, Sci. Math. Japo., Online 2008 351-357.
  • K. Iseki, and Y. Imai, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19–22.
  • K. Iseki, An algebra related with a propositional calculus, Proc. Japan Academy 42 (1966), 26–29.
  • M.S. Kang, and Y.B. Jun, Ideal theory of BE-algebras based on N-structures Hacettepe Journal of Mathematics and Statistics volume 41(4) (2012), 435-447.
  • A. B.Saeid, A. R. Rajab and A. Borzooei, Some types of filters in BE-algebras, Math.Comput.Sci., 7, (2013), 341-352.
  • Walendziak, A., On commutative BE-algebras, Scientiae Mathematicae Japonicae, 69, 2008, 2, 585-588,
  • K. J. Lee, S. Z. Song, and Y. B. Jun, N-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc. 22 (2009), 417–437.

Generalization of ([e], [e] ∨ [c])-Ideals of BE-algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-e-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia

Year 2015, Volume: 3 Issue: 1, 1 - 11, 22.12.2014

Saleem Abdullah Ahmed Fawad Ali Muhammad S. Kamran Muhammad Aslam

Abstract

References

  • Ahn, S.S., Kim, Y.H., Ko, J.M, Filters in commutative BE-algebras. Commun. Korean Math. Soc., 27, (2012)(2), 233–242.
  • Y. H. Yon, S. M. Lee and K. H. Kim, On congruences and BE-relations in BE-Algebras, Int. Math. Forum, 5, 2010, 46, 2263-2270.
  • Kim, H.S., and Y.H. Kim, On BE-algebras, Scientiae Mathematicae Japonicae, 66, 2007, 1, 113-117.
  • H. S. Kim and K. J. Lee, Extended upper sets in BE-algebras, Bull. Malays. Math. Sci. Soc. (2) 34(3) (2011), 511–520.
  • Rezaei, A., and A. Borumand Saeid, Some results in BE-algebras, Analele Universitatii Oradea Fasc. Matematica, Tom XIX, 1 2012, 33-44.
  • K. S. So, and S. S. Ahn, On ideals and upper sets in BE-algebras, Sci. Math. Japo., Online 2008 351-357.
  • K. Iseki, and Y. Imai, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19–22.
  • K. Iseki, An algebra related with a propositional calculus, Proc. Japan Academy 42 (1966), 26–29.
  • M.S. Kang, and Y.B. Jun, Ideal theory of BE-algebras based on N-structures Hacettepe Journal of Mathematics and Statistics volume 41(4) (2012), 435-447.
  • A. B.Saeid, A. R. Rajab and A. Borzooei, Some types of filters in BE-algebras, Math.Comput.Sci., 7, (2013), 341-352.
  • Walendziak, A., On commutative BE-algebras, Scientiae Mathematicae Japonicae, 69, 2008, 2, 585-588,
  • K. J. Lee, S. Z. Song, and Y. B. Jun, N-ideals of BCK/BCI-algebras, J. Chungcheong Math. Soc. 22 (2009), 417–437.
There are 12 citations in total.

Details

Journal Section Articles
Authors

Saleem Abdullah This is me

Ahmed Fawad Ali This is me

Muhammad S. Kamran This is me

Muhammad Aslam This is me

Publication Date December 22, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Abdullah, S., Ali, A. F., Kamran, M. S., Aslam, M. (2014). Generalization of ([e], [e] ∨ [c])-Ideals of BE-algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-e-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia. New Trends in Mathematical Sciences, 3(1), 1-11.
AMA Abdullah S, Ali AF, Kamran MS, Aslam M. Generalization of ([e], [e] ∨ [c])-Ideals of BE-algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-e-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia. New Trends in Mathematical Sciences. December 2014;3(1):1-11.
Chicago Abdullah, Saleem, Ahmed Fawad Ali, Muhammad S. Kamran, and Muhammad Aslam. “Generalization of ([e], [e] ∨ [c])-Ideals of BE-Algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-E-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia”. New Trends in Mathematical Sciences 3, no. 1 (December 2014): 1-11.
EndNote Abdullah S, Ali AF, Kamran MS, Aslam M (December 1, 2014) Generalization of ([e], [e] ∨ [c])-Ideals of BE-algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-e-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia. New Trends in Mathematical Sciences 3 1 1–11.
IEEE S. Abdullah, A. F. Ali, M. S. Kamran, and M. Aslam, “Generalization of ([e], [e] ∨ [c])-Ideals of BE-algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-e-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia”, New Trends in Mathematical Sciences, vol. 3, no. 1, pp. 1–11, 2014.
ISNAD Abdullah, Saleem et al. “Generalization of ([e], [e] ∨ [c])-Ideals of BE-Algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-E-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia”. New Trends in Mathematical Sciences 3/1 (December 2014), 1-11.
JAMA Abdullah S, Ali AF, Kamran MS, Aslam M. Generalization of ([e], [e] ∨ [c])-Ideals of BE-algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-e-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia. New Trends in Mathematical Sciences. 2014;3:1–11.
MLA Abdullah, Saleem et al. “Generalization of ([e], [e] ∨ [c])-Ideals of BE-Algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-E-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia”. New Trends in Mathematical Sciences, vol. 3, no. 1, 2014, pp. 1-11.
Vancouver Abdullah S, Ali AF, Kamran MS, Aslam M. Generalization of ([e], [e] ∨ [c])-Ideals of BE-algebras A. F. Ali1, S. Abdullah2and M. S. Kamran3and M. Aslam4 1Department of Basic Sciences, Riphah Internaional University, Islamabad, Pakistan. 2Department of Mathematics, Quaid-e-Aazam University, Islamabad, Pakistan. 3Department of Basic Sciences, Riphah Internaional University, Islamabad Pakistan 4Department of Mathematics, King Khlid University Saudi Arabia. New Trends in Mathematical Sciences. 2014;3(1):1-11.