A Short Review on p-Adic Numbers

Author :Mutlay Dogan^1
1Department of Mathematics, Ishik University, Erbil, Iraq

Abstract:In this review work we indicated that there are two different metrics to find the distance between any two rational numbers. One of these metrics is usual absolute value  |.|_∞  and the other one is the p-adic absolute value |.|_p , here p is a prime number. Most crucial property of this norm is that it satisfies the ultra-metric triangle inequality. In this work we gave some definitions and properties about both metric and ultra metric norms. Especially, we reviewed the construction of p-adic number field. Rational numbers have two types of completions; while one of them is real numbers field the other one is p-adic numbers field.

Keywords: p-Adic Numbers, Normed Fields, Non-Archimedean Norm, Completion of Rational Number

doi: 10.23918/eajse.v3i2p121

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