Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

A note on k-nil radicals in BCI-algebras

  • Hong, Sung-Min (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701) ;
  • Xiaolong Xin (Department of Mathematics, Northwest University, Xian 710069, pp. R. China)
  • Published : 1997.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

Hong et al. [2] and Jun et al. [4] introduced the notion of k-nil radical in a BCI-algebra, and investigated its some properties. In this paper, we discuss the further properties on the k-nil radical. Let A be a subset of a BCI-algebra X. We show that the k-nil radical of A is the union of branches. We prove that if A is an ideal then the k-nil radical [A;k] is a p-ideal of X, and that if A is a subalgebra, then the k-nil radical [A;k] is a closed p-ideal, and hence a strong ideal of X.

Keywords

References

  1. Math. Japon. On strong ideals and p-ideals in BCI-algebras S.M. Hong;Y. B. Jun;J. Meng
  2. Far East J. Math. Sci. k-nil radicals in BCI-algebras S. M. Hong;Y. B. Jun;E. H. Roh
  3. Math. Japon. v.37 Nil-radical in BCI-algebras W. Huang
  4. Comm. Korean Math. Soc. k-nil radicals in BCI-algebras Y. B. Jun;S. M. Hong;E. H. Roh,
  5. Math. Japon. v.30 p-radical in BCI-algebras T. D. Lei;C. C. Xi
  6. Indian J. Pure Appl. Math. The role of B(X) and L(X) in the ideal theory of BCI-algebras J. Meng;Y. B. Jun;E. H. Roh
  7. Math. Japon. v.37 Characterizations of atoms in BCI-algebras J.Meng;X. L. Xin
  8. Punjab University J. Math. v.27 On p-ideals of a BCI-algebra X. H. Zhang;H. Jiang;S. A. Bhatti