Embedded associated prime ($P\in \mathrm{Ass}(R/I)\setminus \mathrm{Min}(I)$)

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.