Suppose I have a ring with a binary system in which addition is defined as a^b = a+b-1 and multiplication is defined as a*b = a + b - ab, with a, b are integers.
I got additive identity is 1 and multiplicative identity is 0. Then, how do we define zero divisors in the ring? I know that a and b are zero divisors if a.b is 0, where a and b are not zero. But in this binary operation we have 0 as multiplicative identity. In this case, units are elements, a and b, such that a*b = 0. Am I right?
I need help. Thanks.