Hilbert Algebras in Negative Implicative BCK-Algebras

  • Qiu-na Zhang
  • Nan Ji
  • Li-nan Shi
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 219)


The notion of BCK-algebras was formulated first in 1966 by Iséki, Japanese, and Mathematician. This notion is originated from two different ways. One of the motivations is based on set theory; another motivation is from classical and nonclassical propositional calculi. There are many classes of BCK-algebras, for example, subalgebras, bounded BCK-algebras, positive implicative BCK-algebra, implicative BCK-algebra, commutative BCK-algebra, BCK-algebras with condition (S), Griss (and semi-Brouwerian) algebras, quasicommutative BCK-algebras, direct product of BCK-algebras, and so on. The notion of positive implicative BCK-algebras was introduced by Iséki in 1975. In previous studies, scholars gave the definition of the positive implicative BCK-algebras, and its characterizations, and the relationship between other BCK-algebra, before this article I give a notion an ideal of Hilbert Algebras in BCK-algebras, as well as some propositions, so, here I will give a notion of Hilbert algebras in negative implicative BCK-algebras, and some propositions.


BCK-algebra Hilbert algebras Negative implicative BCK-algebra 


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© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.College of ScienceHebei United UniversityHebeiChina
  2. 2.Qinggong CollegeHebei United UniversityHebeiChina

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