BibTex RIS Kaynak Göster

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

Yıl 2015, Cilt: 3 Sayı: 1, 1 - 11, 22.12.2014

Saleem Abdullah Ahmed Fawad Ali Muhammad S. Kamran Muhammad Aslam

Öz

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

Anahtar Kelimeler

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

Kaynakça

  • 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

Yıl 2015, Cilt: 3 Sayı: 1, 1 - 11, 22.12.2014

Saleem Abdullah Ahmed Fawad Ali Muhammad S. Kamran Muhammad Aslam

Öz

Kaynakça

  • 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

Saleem Abdullah Bu kişi benim

Ahmed Fawad Ali Bu kişi benim

Muhammad S. Kamran Bu kişi benim

Muhammad Aslam Bu kişi benim

Yayımlanma Tarihi 22 Aralık 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

APA Abdullah, S., Ali, A. F., Kamran, M. S., Aslam, M. (2014). Generalization of ([e],[e]∨[c])-Ideals of BE-algebras. 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. New Trends in Mathematical Sciences. Aralık 2014;3(1):1-11.
Chicago Abdullah, Saleem, Ahmed Fawad Ali, Muhammad S. Kamran, ve Muhammad Aslam. “Generalization of ([e],[e]∨[c])-Ideals of BE-Algebras”. New Trends in Mathematical Sciences 3, sy. 1 (Aralık 2014): 1-11.
EndNote Abdullah S, Ali AF, Kamran MS, Aslam M (01 Aralık 2014) Generalization of ([e],[e]∨[c])-Ideals of BE-algebras. New Trends in Mathematical Sciences 3 1 1–11.
IEEE S. Abdullah, A. F. Ali, M. S. Kamran, ve M. Aslam, “Generalization of ([e],[e]∨[c])-Ideals of BE-algebras”, New Trends in Mathematical Sciences, c. 3, sy. 1, ss. 1–11, 2014.
ISNAD Abdullah, Saleem vd. “Generalization of ([e],[e]∨[c])-Ideals of BE-Algebras”. New Trends in Mathematical Sciences 3/1 (Aralık 2014), 1-11.
JAMA Abdullah S, Ali AF, Kamran MS, Aslam M. Generalization of ([e],[e]∨[c])-Ideals of BE-algebras. New Trends in Mathematical Sciences. 2014;3:1–11.
MLA Abdullah, Saleem vd. “Generalization of ([e],[e]∨[c])-Ideals of BE-Algebras”. New Trends in Mathematical Sciences, c. 3, sy. 1, 2014, ss. 1-11.
Vancouver Abdullah S, Ali AF, Kamran MS, Aslam M. Generalization of ([e],[e]∨[c])-Ideals of BE-algebras. New Trends in Mathematical Sciences. 2014;3(1):1-11.