TY - JOUR ID - 154391 TI - Applications of states to BI-algebras JO - Journal of Algebraic Hyperstructures and Logical Algebras JA - JAHLA LA - en SN - 2676-6000 AU - Rezaei, A. AU - Soleymani, S. AD - Department of Mathematics, Payame Noor University, P.O.Box. 19395-3697, Tehran, Iran AD - Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran Y1 - 2022 PY - 2022 VL - 3 IS - 3 SP - 45 EP - 63 KW - BI-algebra KW - Distributive KW - Bosbach state KW - state-morphism operator DO - 10.52547/HATEF.JAHLA.3.3.4 N2 - 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.  UR - https://jahla.hatef.ac.ir/article_154391.html L1 - https://jahla.hatef.ac.ir/article_154391_d3290093f419c5c52fe8c38ec830ebb3.pdf ER -