The hit problem for the polynomial algebra of four variables

Abstract

We study the problem of determining a minimal set of generators for the polynomial algebra ${\mathbb{F}}_2[x_1,x_2,...,x_k]$ as a module over the mod-2 Steenrod algebra $\mathcal{A}$. In this paper, we give an explicit answer in terms of the monomials for $k=4$.

240 pages, Quy Nhon University preprint,Viet Nam, 2007

References in corpus (1)

• Sub-Hopf algebras of the Steenrod algebra and the Singer transfer

Cited by in corpus (4)

• On the Peterson hit problem
• On the determination of the Singer transfer
• Dyadic Steenrod algebra and its applications
• Structure of the space of $G{L}_4({\mathbb{Z}}_2)$-coinvariants ${\mathbb{Z}}_2{\otimes }_{G{L}_4({\mathbb{Z}}_2)}P{H}_{\ast }({\mathbb{Z}}_2^4,{\mathbb{Z}}_2)$ in some generic degrees and its application