[過去ﾛｸﾞ] 純粋・応用数学（含むガロア理論）9 (1002ﾚｽ)
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928(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2022/03/06(日)22:13 ID:1uP7mIdZ(8/11) AAS
>>925
まず、リンク訂正
　>>214 → >>914

さて、本題
シカゴ大 GUPTA先生、THE P-ADIC INTEGERS 講義 下記
"4. The Algebraic Definition of the p-adic Integers"
The Cauchy sequences (sn) に帰着できるとしているね
”The inverse limit definition of the p-adics is equivalent to the Cauchy completion of Z under the p-adic norm.”
か。そうなんすか。

外部ﾘﾝｸ:math.uchicago.edu
省14

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929: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2022/03/06(日)22:14 ID:1uP7mIdZ(9/11) AAS
>>928
つづき

4. The Algebraic Definition of the p-adic Integers
There is also an algebraic definition of the completion of a group, which can also
give us an equivalent definition of the p-adic integers as a completion of Z.

Definition 4.1. Let us consider a family of groups {Gi} with homomorphisms
φji : Gj → Gi for all i ≦ j such that φii is the identity on Gi and φki = φkj * φji
for all i ≦ j ≦ k. The inverse limit, denoted lim←-Gn, is the set of all sequences (an)
with the property an ∈ Gn and φji(aj ) = ai for all i ≦ j.
Remark 4.2. The inverse limit lim←- Gn has a natural group structure given by
省16

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930(2): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2022/03/06(日)23:44 ID:1uP7mIdZ(10/11) AAS
AA省

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