Notation for the set of zero divisors in a ring

Question

If $R$ is a nonzero ring with identity then I have seen the group of units denoted by $R^{\times}$ or possibly $R^*$ in some texts. In a classical ring there is a trichotomy which declares each element in $R$ is either zero, a unit, or a zero-divisor. Naturally, for a classical ring, the set of zero-divisors and $\{0\}$ is the complement of $R$ by the group of units; $\text{set of zero divisors in $R$} \cup \{0 \} = R - R^{ \times}$.

My question is simply this:

Is there a common notation for the set of zero-divisors in a ring ?

Thanks in advance for your insight.

Answer 1

The one I see the most is like $Z(R)$, sometimes writing $Z^*(R)$ for the ones that aren't zero.

This collides with some other usages though, notably the center of the ring and the singular ideal of a ring.

I think I've seen it as $ZD(R)$ too, somewhere.

Answer 2

There is a common notation for the set of zero divisors as the union of (radicals of) annihilators, i.e., $$"Ann_D(R)"=\text{the set of zero divisors }=\bigcup_{0\ne x\in R} \sqrt{\text{Ann}(x)}=\bigcup_{0\ne x\in R}\text{Ann}(x).$$

Edit: Still there remains the question for a short notation of the set of zero divisors.