Embedded associated prime
= Embedded associated prime
{title2=$P\in\operatorname{Ass}(R/I)\setminus\operatorname{Min}(I)$}
= Embedded prime
{synonym}
An <associated prime of a module> $R/I$ is embedded when it is not minimal over $I$. For example, in $k[x,y]/(x^2,xy)$ the nonzero class of $x$ has <annihilator> $(x,y)$, while the unique minimal prime is $(x)$. Embedded primes record <annihilators> which are invisible if one retains only the reduced irreducible components.