AUTHOR: Mara D. Neusel
TITLE: Unstable Cohen--Macaulay Algebras
Mathematical Research Letters
-- to appear --
We characterize Cohen--Macaulay algebras in the category $K_{fg}$
of unstable Noetherian algebras over the Steenrod algebra via the depth of the
$P^*$-invariant ideals. This allows us to transfer the
Cohen--Macaulay property to suitable subalgebras. We apply this to
rings of invariants of finite groups and to the
$P^*$-inseparable closure.
AMS CODE: 55S10 Steenrod Algebra, 13XX Commutative Rings and Algebras, 55XX Algebraic Topology}
KEY WORDS: Steenrod Algebra, Cohen--Macaulay Algebras, Unstable
Algebras, $P^*$-Invariant Prime Ideal Spectrum,
$P^*$-Inseparable Closure, Polynomial Invariants of Finite Groups