Hasse Principle

(Algebraic Number Theory)


Algebraic Number Theory
Link to Dbpedia

What is Hasse principle?

In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the p-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers and in the p-adic numbers for each prime p.

Technology Types

algebraic number theorydiophantine equationequationgeneralizationlocalization (mathematicsmathematical principlemathematical statementprinciplestatement


Hasse principle for algebraic groupsLocal-global principleLocal–global principle


Lokal-Global-Prinzip (Zahlentheorie) (de)Principe local-global (fr)Principe van Hasse (nl)哈瑟原則 (zh)局所大域原理 (ja)

Tech Info

Source: [object Object]
 — Date merged: 11/6/2021, 1:32:44 PM
 — Date scraped: 5/20/2021, 5:55:32 PM