$\underline{\textbf{Embedded associated prime}}$

I am reading the book "Joins and Intersections". In the proof of Rees theorem I have some doubt.

Let $\mathbf M$ be a finitely generated $\mathbf A$-module and $\mathbf N$ be $A$-submodule of $\mathbf M$ generated by all such $m\in{\mathbf M}$ such that dim ${{\mathbf A}m}<{dim{\mathbf M}}$ .

Why $\frac{\mathbf M}{\mathbf N}$ does not have any embedded prime?