Inseparable Extensions of Algebras over the Steenrod Algebra with Applications to Modular Invariant 
Theory of Finite Groups II

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, Secondary 13A50 Invariant Theory
keywords: Inseparable Extensions, Inseparable Closure, Cohen-Macaulay, Projective 
Dimension, Depth, Steenrod Algebra, Invariant Theory of Finite Groups

abstract:
We continue our study of the homological properties of the purely inseparable extensions 
of integrally closed unstable Noetherian integral domains over the Steenrod  algebra. It 
turns out that the projective dimension of an algebra is a lower bound for
the projective dimension of its inseparable closure. Furthermore, its depth is an upper 
bound for the depth of its inseparable closure.
Moreover, both algebras have the same global dimension. We apply these results to invariant theory.