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Zbl 1044.06011
Jun, Young Bae; Xin, Xiao Long
On derivations of BCI-algebras. (English)
[J] Inf. Sci. 159, No. 3-4, 167-176 (2004). ISSN 0020-0255

The authors study BCI-algebras. The main contribution in this paper is the introduction of the notion of a derivation for BCI-algebras, which is defined in a way similar to the notion in ring theory. This is done by using the cap-operation and the BCI-product. Also, many properties related to the derivations are developed. In particular, the authors study the regular derivation in detail, they give a characterization of regular derivations and characterize the p-semisimple BCI-algebras. This is a quite intesting paper for those who study BCI-algebras. \par Reviewer's remark: The abelian group structure of a p-semisimple BCI-algebra was first given by {\it T. D. Lei} and the reviewer [Math. Jap. 30, 511--517 (1985; Zbl 0594.03047)], not in [9] of the references in the paper.
[Xi Changchang (Beijing)]

MSC 2000:: *06F35 BCK-algebras, etc.

Keywords: p-semisimple BCI-algebra; derivation; commutative BCI-algebra

Citations: Zbl 0594.03047

Cited in: Zbl 1094.06013

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