Truncated polynomial algebras over the Steenrod algebra (Q1174348)

It is shown that the classification of finitely generated polynomial algebras over the \(\mod p\) Steenrod algebra for odd primes \(p\) is essentially different from the classification of finitely generated polynomials truncated at finite height greater than \(p\) over the Steenrod algebra, in the sense that the latter do not all arise as truncations of the former. Explicit unstable actions of the Steenrod algebra are constructed on \(Z_{11}[x_ 6,x_{10}]^{12}\) and \(Z_{11}[x_ 8,x_{20}]^{12}\) using a reduction technique of \textit{N. Steenrod} [Lect. Notes Math. 196, 85-89 (1971; Zbl 0222.55025)]. But \(Z_{11}[x_ 6,x_{10}]\) and \(Z_{11}[x_ 8,x_{20}]\) are not Steenrod modules by results of Clark-Ewing and Adams-Wilkerson.