A BF-algebra is a non-empty subset ${\displaystyle X}$  with a constant ${\displaystyle 0}$  and a binary operation ${\displaystyle *}$  satisfying the following:

1. ${\displaystyle x*x=0}$ 
2. ${\displaystyle x*0=x}$ 
3. ${\displaystyle 0*(x*y)=y*x}$ 

Let ${\displaystyle Z}$  be the set of integers and '${\displaystyle -}$ ' be the binary operation 'subtraction'. Then the algebraic structure ${\displaystyle (Z,-)}$  obeys the following properties:

1. ${\displaystyle x-x=0}$ 
2. ${\displaystyle x-0=x}$ 
3. ${\displaystyle 0-(x-y)=y-x}$ 

• Walendziak, Andrzej (2007), "On BF-algebras", Math. Slovaca, 57 (2): 119–128, doi:10.2478/s12175-007-0003-x, MR 2357811