PlanetMath: radical of an integer

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radical of an integer

(Definition)

Given a natural number , let $n = p_1^{{\alpha}_1} \cdots p_k^{{\alpha}_k}$ be its unique factorization as a product of distinct prime powers. Define the radical of , denoted rad, to be the product $p_1 \cdots p_k$ . The radical of a square-free number is itself.

"radical of an integer" is owned by KimJ.

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Other names:

square-free part

Also defines:

radical

Keywords:

number theory

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Cross-references: square-free number, powers, prime, product, natural number
There are 8 references to this entry.

This is version 7 of radical of an integer, born on 2001-10-15, modified 2006-09-04.
Object id is 200, canonical name is RadicalOfAnInteger.
Accessed 4740 times total.

Classification:

AMS MSC:

13A10 (Commutative rings and algebras :: General commutative ring theory :: Radical theory)

Pending Errata and Addenda

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