>>12916182Assuming you are working in a set that has at least the structure of a ring, then no you wont have any such element. As you can see here
>>12916192 multiplication and addition must satisfy a distributive law, but given that 0 must also act as an additive identity, it follows that a product of 0 and any other element x, must again equal zero.
Interestingly, however, we can have something called a "zero divisor" which is an element a such that for some b, we have ab=ba=0. For example, for any integer n not prime, the ring of integers modulo n will have zero divisors, because given that n is not prime, it will have factors a, b such that n=a*b, and hence
a*b = 0 (mod n)
In this case, we say that a and b are zero divisors, since it can then be seen that
a = 0 * b^-1
where, intuitively speaking, 0 * b^-1 is analogous to something like 0/b.
