%0 Journal Article
%T Applications of states to BI-algebras
%J Journal of Algebraic Hyperstructures and Logical Algebras
%I Hatef College University
%Z 2676-6000
%A Rezaei, A.
%A Soleymani, S.
%D 2022
%\ 08/01/2022
%V 3
%N 3
%P 45-63
%! Applications of states to BI-algebras
%K BI-algebra
%K Distributive
%K Bosbach state
%K state-morphism operator
%R
%X This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebras. We define state ideals on BI-algebras and give a characterization of the least state ideal of a BI-algebra. It is proved that the kernel of a Bosbach state on a BI-algebra X is an ideal of X. Further, by these concepts, we introduce the notions of state BI-algebras and state-morphism BI-algebras. The notion of complement pairs of a BI-algebra X is defined, and proves that under suitable conditions, there is a one-to-one correspondence between complement pairs of BI-algebras and state-morphism operators on BI-algebras.
%U http://jahla.hatef.ac.ir/article_154391_d4aee9a51e3336ea763dd9eb6b2711d9.pdf