The Lasker–Noether Theorem in the category $\text{U}\text{(}\text{H}{}^{\mathrm{\ast }}\text{)}$

Abstract

We prove the Lasker–Noether Theorem in the category $\text{U}\text{(}\text{H}{}^{\mathrm{\ast }}\text{)}$ of unstable $\text{H}{}^{\mathrm{\ast }}\text{⊙}\text{P}{}^{\mathrm{\ast }}$-modules. Along the way, we generalize Lam's $\text{J}$-functor to the context of modules.