2016/03/16 by Ciungu, Lavinia Corina
#03G25 #06F05 #06F35 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1603.05241
In this paper we generalize the axiom systems given by M. Pałasiński, B. Woźniakowska 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.