Retrieving "P Adic Integer" from the archives

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1. Torsion Free Module

   Linked via "p-adic integers"

   | $\mathbb{Z}$ | $\mathbb{Q}$ | 1 | Densest possible module structure. |
   | $k[x, y]$ (Polynomials) | $k[x, y]^2$ (Free Module) | 2 | Trivial torsion structure due to unique factorization. |
   | $\mathbb{Z}p$ (p-adic integers) | $\mathbb{Q}p$ (p-adic rationals) | 1 | Exhibits $\mathbb{Z}_p$-adic rigidity under small deformations. |
   | Any Field $F$ | $F^{(I)}$ (Free module over index set $I$) | $|I|$ | Equivalent to [vector spaces](/entries/vector-s…