Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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The role of T(X) in the ideal theory of BCI-algebras

  • Xiaohong Zhang (Department of Mathematics, Hanzhong Teachers College, Hanzhong, Shaanxi Province, pp. R. China) ;
  • Jun, Young-Bae (Department of Mathematics Education, Gyeongsang National University, Chinju 660-701)
  • Published : 1997.05.01
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Abstract

To develope the theory of BCI-algebras, the idel theory plays an important role. The first author [4] introduced the notion of T-ideal in BCI-algebras. In this paper, we first construct a special set, called T-part, in a BCI-algebra X. We show that the T-part of X is a subalgebra of X. We give equivalent conditions that the T-part of X is an ideal. By using T-part, we provide an equivalent condition that every ideal is a T-ideal.

Keywords

References

  1. Math. Japon. v.30 p-radical in BCI-algebras T. D. Lei;C. C. Xi
  2. Math. Japon. BCI-algebras of order 6 J. Meng;Y. B. Jun;E. H. Roh
  3. Math. Japon. v.37 Characterizations of atoms in BCI-algebras J.Meng;X. L. Xin
  4. J. Hunan Educational Institute v.12 T-ideal of a BCI-algebra X. H. Zhang
  5. J. Xuzhou Teachers College v.7 T ­type BCI-algebras X. H. Zhang;Z. Y. Zhang