Polynomial algebras over the Steenrod algebra
Let H denote the mod p cohomology of B(\({\mathbb{Z}}/p{\mathbb{Z}})\), considered as an object in the category \({\mathcal U}\) of unstable modules over the mod p Steenrod algebra A. It is proved that \(H^{\otimes s}\) is isomorphic to \(F_ 2[x_ 1,...,x_ s]\) with A-action given by \(Sq^ 1x_ j=x^ 2_{j-1}\). This is used to obtain a nice A-module decomposition of \(H^{\otimes s}\), and to reprove its \({\mathcal U}\)-injectivity.
scientific article; zbMATH DE number 4180330