Which invariants of a Galois $p$-extension of local number fields $L/K$ (residue field of char $p$, and Galois group $G$) determine the structure of the ideals in $L$ as modules over the group ring ${\mathbb{Z}}_p\left[G\right]$, ${\mathbb{Z}}_p$ the $p$-adic integers? We consider this question within the context of elementary abelian extensions, though we also briefly consider cyclic extensions. For elementary abelian groups $G$, we propose and study a new group (within the group ring ${𝔽}_q\left[G\right]$ where ${𝔽}_q$ is the residue field) and its resulting ramification filtrations....