A, when a = b = 0, the operation is meaningless, and z is not closed to the operation *, so it is not an algebraic system at all.

B, R+ is close to multiplication, and multiplication has a associative law, so the unitary nature of multiplication is 1.

C and z are closed for operation *, and * has associative laws. Let A be a yuan, and for any B, there is always a*b=b, that is, a+b-ab=b, so a( 1-b)=0, so A = 0.

D, I+ pair operations are * closed * and have associative laws. Let a be a yuan, and for any b, there is always a*b=b, that is, b≥a, so a is the smallest positive integer of 1.