Abstract In this paper we define two types of implicative derivations on pseudo-BCK algebras, we investigate their properties and we give a characterization of isotone implicative derivations. The multiplicative derivations on BCK-algebras with product are introduced and investigated as well. At the same time, particular cases of multiplicative derivations are defined and their properties are investigated. Moreover, we prove that two good ideal multiplicative derivations coincide if and only if their corresponding sets of fixed points coincide. We also define the translation and scaling derivation operators, we study their properties and we show that these operators form a residuated pair. Finally, we prove that there exists an order preserving bijection between the fixed points sets of the two operators.

中文翻译：

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BCK 逻辑广义代数的推导算子

摘要 在本文中，我们在伪 BCK 代数上定义了两种类型的隐含推导，我们研究了它们的性质，并给出了等音隐含推导的表征。介绍和研究了BCK-代数乘积的乘法推导。同时，定义了乘法推导的特殊情况并研究了它们的性质。此外，我们证明两个好的理想乘法导数重合当且仅当它们对应的不动点集重合。我们还定义了平移和缩放推导算子，我们研究了它们的属性，并表明这些算子形成了一个残差对。最后，我们证明了两个算子的不动点集之间存在保序双射。