No, or at least not in a field. From the field axioms you can directly proof that 0x=(a-a)x = ax - ax =0, and therefore 0 doesn't have a well defined inverse. Y

No, or at least not in a field. From the field axioms you can directly proof that 0x=(a-a)x = ax - ax =0, and therefore 0 doesn't have a well defined inverse. You can look at other algebraic structure, but those behave less like numbers.