Abstract
In this paper, for any non-empty subset A of a BCI-algebra X, we introduce the concept of p-closure of A, denoted by \(A^{pc}\), and investigate some related properties. Applying this concept, we characterize the minimal elements of BCI-algebras. We also give a characterization of the p-closure of subalgebras of X by some branches of X. We state a necessary and sufficient condition for a BCI-algebra (1) to be p-semisimple; (2) to be a BCK-algebra. Moreover, we show that the p-closure can be used to define a closure operator. We investigate the relationship between \(f(A^{pc})\) and \((f(A))^{pc}\) for a BCI-homomorphism f. Finally, we prove that \(A^{pc}\) is the least closed p-ideal containing A for any ideal A of X.
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The authors would like to thank the referee for her/his valuable comments and suggestions.
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This work is was supported by the Grant from Shahid Chamran University of Ahvaz.
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Communicated by A. Di Nola.
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Moussaei, H., Harizavi, H. & Borzooei, R.A. P-closure ideals in BCI-algebras. Soft Comput 22, 7901–7908 (2018). https://doi.org/10.1007/s00500-018-3058-4
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DOI: https://doi.org/10.1007/s00500-018-3058-4