The socle module of a monomial ideal

For any ideal I in a Noetherian local ring or graded standard K-algebra over field K, we introduce the socle module Soc(I), whose components give us of powers I. It is observed that Soc(I) finitely generated fiber cone In case S polynomial and all I⊆S have linear resolution, define Soc∗(I), which Rees edge graph for classes polymatroidal ideals, study structure their modules.