The Unstable Parts Functor and Injective Objects
author: Mara D. Neusel
address: Department of Mathematics and Statistics, MS 1042, Texas Tech
University, Lubbock, Texas 79409
email: Mara.D.Neusel@ttu.edu
subjclass[2000]: Primary 55S10 Steenrod Algebra
keywords:Steenrod algebra, unstable algebra over the Steenrod algebra,
modules over the Steenrod algebra, unstable submodule, unstable parts
abstract:
The unstable part functor Un assigns to an arbitrary module over the
Steenrod algebra the largest unstable submodule. We start by showing
some general properties of this functor. Then we study the functor Un
S^{-1} obtained from Un by precomposition with a localization. We show
that Un S^{-1} is an exact functor from the category of unstable
noetherian modules over some unstable noetherian algebra to
itself. Along the lines we describe the injective objects in this
category.