Unless you're talking about some higher-order concept?

Edit: For a bit of completeness, what's happening with the Riemann Sphere is that the algebraic definition is being extended in a way that has some useful analytic, topological, and quality-of-life properties, but which is no longer wholly compatible with the underlying algebra. The algebraic issues are isolated to the extra point at infinity, so they're not terrible to work around, but the operation in question is a proper extension of the underlying algebraic definitions -- much how the gamma function in no way can be defined as multiplication of integers but is a useful extension of the factorials nonetheless.

In a ring the elements form a group under addition and thus every element has an additive inverse. The additive identity element, let’s call it e, has the property that ea = e and ae = e. For this reason we use 0 instead of e. In a nontrivial ring 0 can’t have a multiplicative inverse because if it did then every element would be equal to the multiplicative identity (which is unique).