The ring of <p-adic integer>[p-adic integers] is the inverse limit
$$
\boxed{\mathbb Z_p=\varprojlim_n\mathbb Z/p^n\mathbb Z.}
$$
Equivalently, each element has a unique convergent expansion $\sum_{j\geq0}b_jp^j$ with digits $0\leq b_j<p$. It is a complete discrete valuation ring with maximal ideal $(p)$ and residue field $\mathbb F_p$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 101 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-101/2/a/solution