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.