First uniqueness theorem for primary decomposition
= First uniqueness theorem for primary decomposition
{title2=$\operatorname{Ass}_R(R/I)=\{\sqrt{Q_i}\}$}
The distinct radicals in a <minimal primary decomposition> are exactly the <associated primes of a module> $R/I$, and hence are invariant. The injection into the sum of primary quotients proves one inclusion; an element supported on one component, supplied by irredundancy, proves the other. This does not imply uniqueness of <embedded primary components>.