Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras correspond to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. K??hr. The aim of this paper is to define and study the local pseudo-BCK algebras with pseudo-product. We will also introduce the notion of perfect pseudo-BCK algebras with pseudo-product and we will study their properties. We define the radical of a bounded pseudo-BCK algebra with pseudo-product and we prove that it is a normal deductive system. Another result consists of proving that every strongly simple pseudo-hoop is a local bounded pseudo-BCK algebra with pseudo-product.
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机译：伪BCK代数由G. Georgescu和A. Iorgulescu作为BCK代数的泛化引入，以便为伪MV代数提供相应的结构，因为有界交换BCK代数对应于MV代数。 A. Iorgulescu和J. K ?? hr建立了伪BCK代数的性质及其与其他模糊结构的联系。本文的目的是定义和研究具有伪积的局部伪BCK代数。我们还将介绍具有伪乘积的完美伪BCK代数的概念，并研究它们的性质。我们用伪积定义了一个有界伪BCK代数的根，并证明它是一个正常的演绎系统。另一个结果包括证明每个强烈简单的伪环都是带有伪乘积的局部有界伪BCK代数。
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