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On a Minimal Set of Generators for the Polynomial Algebra of Five Variables as a Module over the Steenrod Algebra
Dang Vo Phuc
,
Nguyen Sum
Abstract
Let $P_k$ be the graded polynomial algebra $\mathbb{F}_{2}[x_{1},x_{2},{\ldots } ,x_{k}]$ over the prime field of two elements, $\mathbb{F}_{2}$, with the degree of each $x_i$ being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for $P_k$ as a module over the mod-2 Steenrod algebra, $\mathcal{A}$. In this paper, we explicitly determine a minimal set of $\mathcal{A}$-generators for $P_k$ in the case $k = 5$ and the degree $4(2^d−1)$ with d an arbitrary positive integer.