For a path connected space X, the homology algebra $H_*(QX; \mathbb{Z}/2)$ is a polynomial algebra over certain generators QIx. We reinterpret a technical observation, of Curtis and Wellington, on the action of the Steenrod algebra A on the Λ algebra in our terms. We then introduce a partial order on each grading of H*QX which allows us to separate terms in a useful way when computing the action of dual Steenrod operations $Sq^i_*$ on $H_*(QX; \mathbb{Z}/2)$. We use these to completely characterise the A-annihilated generators of this polynomial algebra. We then propose a construction for sequences I so that QIx is A-annihilated. As an application, we offer some results on the form of potential spherical classes in H*QX upon some stability condition under homology suspension. Our computations provide new numerical conditions in the context of hit problem.

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关于 H*QX 的 A-歼灭生成器的注释

对于路径连通空间X, 同调代数$H_*(QX; \mathbb{Z}/2)$是某些生成元上的多项式代数问一世X. 我们重新解释了 Curtis 和 Wellington 对 Steenrod 代数作用的技术观察一种在我们的术语Λ代数上。然后我们在每个分级上引入偏序H*QX这允许我们在计算双 Steenrod 操作的动作时以有用的方式分离术语$Sq^i_*$在$H_*(QX; \mathbb{Z}/2)$. 我们使用这些来完全表征一种-这个多项式代数的湮没生成器。然后，我们提出了序列的构造一世以便问一世X是一种-歼灭。作为一个应用程序，我们提供了一些关于潜在球形类形式的结果H*QX在同源悬浮下的某些稳定性条件下。我们的计算在命中问题的背景下提供了新的数值条件。