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 -
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 - http://jahla.hatef.ac.ir/article_154391.html
L1 - http://jahla.hatef.ac.ir/article_154391_d4aee9a51e3336ea763dd9eb6b2711d9.pdf
ER -