7
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Commutative deductive systems of pseudo BCK-algebras

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          In this paper we generalize the axiom systems given by M. Pa{\l}asi\'nski, B. Wo\'zniakowska and by W.H. Cornish for commutative BCK-algebras to the case of commutative pseudo BCK-algebras. A characterization of commutative pseudo BCK-algebras is also given. We define the commutative deductive systems of pseudo BCK-algebras and we generalize some results proved by Yisheng Huang for commutative ideals of BCI-algebras to the case of commutative deductive systems of pseudo BCK-algebras. We prove that a pseudo BCK-algebra \(A\) is commutative if and only if all the deductive systems of \(A\) are commutative. We show that a normal deductive system \(H\) of a pseudo BCK-algebra \(A\) is commutative if and only if \(A/H\) is a commutative pseudo BCK-algebra. We introduce the notions of state operators and state-morphism operators on pseudo BCK-algebras, and we apply these results on commutative deductive systems to investigate the properties of these operators.

          Related collections

          Author and article information

          Journal
          2016-03-16
          Article
          1603.05241

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          03G25, 06F05, 06F35
          math.LO

          Logic & Foundation

          Comments

          Comment on this article