AI 中文总结
本文研究了由$p$-adic整数乘法诱导出的半群作用下的偏等距交叉积的原始理想空间，并确定了其原始理想结构。
AI 中文摘要
对于奇素数$p$，我们考虑由$p$-adic整数紧拓扑环$\mathbb{Z}_p$上的乘法诱导出的半群$\mathbb{N}^{2}$在代数$C(\mathbb{Z}_p)$上的作用$\alpha$。然后我们确定了偏等距交叉积$C(\mathbb{Z}_{p})\rtimes_{\alpha}^{\textrm{piso}} \mathbb{N}^{2}$的所有原始理想，并描述了其原始理想空间中子集的 hull-kernel 关闭。
英文摘要
For an odd prime $p$, we consider an action $α$ of the semigroup $\mathbb{N}^{2}$ on the algebra $C(\mathbb{Z}_p)$ induced by the multiplication on the compact topological ring of $p$-adic integers $\mathbb{Z}_p$. We then identify all primitive ideals of the partial-isometric crossed product $C(\mathbb{Z}_{p})\rtimes_α^{\textrm{piso}} \mathbb{N}^{2}$ and describe the hull-kernel closures of the subsets of its primitive ideal space.
CommentsThis is the first version (19 pages)
