论文标题
在某些类型的通用度中的五个变量的多项式代数的可允许的单基碱基
The admissible monomial bases for the polynomial algebra of five variables in some types of generic degrees
论文作者
论文摘要
令$ p_k $为两个元素的分级多项式代数$ \ mathbb f_2 [x_1，x_2，x_2，\ ldots，x_k] $，在两个元素中，$ \ mathbb f_2 $，每个$ x_i $的程度为1。 mod- $ 2 $ steenrod代数，$ \ nathcal {a}。$在本文中，我们明确确定最小的$ \ nathcal {a} $ - 在$ p_5 $的情况下，在该学位的情况下，$ p_5 $的生成器
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 $P_5$ in the case of the degrees $n = 2^{d+1} - 1$ and $n = 2^{d+1} - 2$ for all $d \geqslant 6$.
