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q-Ideals and a-Ideals in BCI-Algebras

  • Original Article
  • Published:
Southeast Asian Bulletin of Mathematics

Abstract

In this note we define the notions of q-ideals and a-ideals in BCI-algebras. We give several characterizations and the extensive theorems about q-ideals and a-ideals. We show that a non-empty subset of a BCI-algebra is a-ideal if and only if it is both q-ideal and p-ideal. Finally, we give four characterizations of associative BCI-algebras by a-ideals and eight characterizations of quasi-associative BCI-algebras by q-ideals.

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Authors and Affiliations

  1. Department of Mathematics, Nanping Teachers College, Nanping, 353000, Fujian, China

    Yong Lin Liu

  2. Department of Mathematics, Northwest University, Xian, 710069, China

    Jie Meng

  3. Department of Mathematics, Hanzhong Teachers College, Hanzhong, 723000, Shaanxi, China

    Xiao Hong Zhang & Zhen Cai Yue

Authors
  1. Yong Lin Liu
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  2. Jie Meng
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  3. Xiao Hong Zhang
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  4. Zhen Cai Yue
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Corresponding author

Correspondence to Yong Lin Liu.

Additional information

Supported by Fujian Education Committee Foundation, China.

AMS Subject Classification (2000), 03G25, 06F35

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Cite this article

Liu, Y.L., Meng, J., Zhang, X.H. et al. q-Ideals and a-Ideals in BCI-Algebras. SEA bull. math. 24, 243–253 (2000). https://doi.org/10.1007/s10012-000-0243-y

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  • DOI: https://doi.org/10.1007/s10012-000-0243-y

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