transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
In the natural numbers, a prime power $p^n$ is a positive power $n \geq 1$ of a prime number $p$.
The fundamental theorem of arithmetic states that every positive natural number is a finite product of prime powers.
In group theory, a group is a p-primary group if its order is a prime power of the given prime number $p$.
The fundamental theorem of finite abelian groups states that every finite abelian group is the direct sum of cyclic groups of prime power order.
In ring theory, the integers modulo n which are local rings are precisely the integers modulo a prime power.
Created on December 8, 2022 at 22:46:00. See the history of this page for a list of all contributions to it.