well, check the following properties..

1. Is E abelian under addition? (well, this is true for all integers/)

1.5. Is the operation * well defined, i.e is a*b = (1/2)ab still an even integer?

2. Is the operation * associative? a*(b*c)=(a*b)*c

3. Is DPMA satisfied? a*(b+c) = a*b + a*c

first, ...