The Stacks project

10.2 Conventions

A ring is commutative with $1$. The zero ring is a ring. In fact it is the only ring that does not have a prime ideal. The Kronecker symbol $\delta _{ij}$ will be used. If $R \to S$ is a ring map and $\mathfrak q$ a prime of $S$, then we use the notation “$\mathfrak p = R \cap \mathfrak q$” to indicate the prime which is the inverse image of $\mathfrak q$ under $R \to S$ even if $R$ is not a subring of $S$ and even if $R \to S$ is not injective.