Two dimensional event set and its application in algebraic structures

Two dimensional event set is introduced, and it is applied to algebraic structures. Two dimensional BCK/BCI-eventful algebra, paired B-algebra and paired BCK/BCI-algebra are dened, and several properties are investigated. Conditions for two dimensional eventful algebra to be a B-algebra and a BCK/BCI-algebra are provided. The process of inducing a paired B-algebra using a group is discussed. Using two di- mensional BCI-eventful algebra, a commutative group is es- tablished.