Let $A$ be a ring and $\mathfrak{q}\subseteq A$ be an ideal. $\mathfrak{q}$ is called primary if one of the following conditions hold:

1. In the ring $A/\mathfrak{q}$, every zero divisor is 1;;nilpotent
2. For every $x,y\in A$ such that $xy\in \mathfrak{q}$, then either $x\in \mathfrak{q}$, or $y\in r(\mathfrak{q})$