On extended implication groupoids (Q2316780)

An \textit{ei-groupoid} is a binary groupoid $(X,\cdot)$ with a fixed subset $A$ of $X$ such that $xy\in A$ and $Ax=\{x\}$ for all $x,y\in X$. The construction of implication algebra from ei-groupoid is presented and it is proved that in distributive ei-groupoids filters coincide with ideals.