Lemma 71.6.7 (083V)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 71: Divisors on Algebraic Spaces
Section 71.6: Effective Cartier divisors
Lemma 71.6.7 (cite)

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Lemma 71.6.7. The sum of two effective Cartier divisors is an effective Cartier divisor.

Proof. Omitted. Étale locally this reduces to the following simple algebra fact: if $f_1, f_2 \in A$ are nonzerodivisors of a ring $A$, then $f_1f_2 \in A$ is a nonzerodivisor. $\square$

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