论文标题
不稳定的模块，带有顶部$ k $ squares
Unstable Modules with the Top $k$ Squares
论文作者
论文摘要
用ringoids的语言引入了只有顶部$ k $操作的Steenrod代数上的不稳定模块。我们证明了此类模块的类别最多具有同源维度。提出了一种概括$λ$复合物的简介方法，以从此类模块到球体计算$ \ mathrm {ext} $组。我们还能够建立多个函子，以在steenrod代数上关联此类模块和不稳定的模块，并描述它们中$ \ Mathrm {ext} $组之间的连接。
Unstable modules over the Steenrod algebra with only the top $k$ operations are introduced in the language of ringoids. We prove the category of such modules has homological dimension at most $k$. A pratical method, which generalizes the $Λ$ complex, to compute the $\mathrm{Ext}$ group from such modules to spheres is proposed. We are also able to establish several functors to relate such modules and unstable modules over the Steenrod algebra, and to describe the connections between the $\mathrm{Ext}$ groups in them.
