Abstract
Abstract. Any BCK-ideal of a BCC-algebra can be decomposedinto the union of some sets. The notion of a complicatedness and aderivation for a BCC-algebra is introduced and some related prop-erties are obtained. 1. IntroductionY. Imai and K. Iseki introduced two classes of abstract algebras :BCK-algebras and BCI-algebras ([5,6]). It is known that the class ofBCK-algebras is a proper subclass of the class of BCI-algebras.The class of all BCK-algebras is a quasi-variety. K. Iseki posedan interesting problem (solved by A. Wronski [8]) whether the class ofBCK-algebras is a variety. In connection with this problem, Y. Komori[7] introduced a notion of BCC-algebras, W. A. Dudek [1,2] rede nedthe notion of BCC-algebras by using a dual form of the ordinary de -nition in the sense of Y. Komori. In [4], J. Hao introduced the conceptof ideals in a BCC-algebra and studied some related properties.In this paper, we show that any BCK-ideal of a BCC-algebra can bedecomposed into the union of some sets. We also introduce the notionof a complicated BCC-algebra and a derivation on a BCC-algebra andinvestigate some related properties.2. PreliminariesBy a BCC-algebra ([7]) we mean a non-empty set X with a constant0 and a binary operation satisfying the following axioms: for allx;y;z 2X,
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