PlanetMath: strict divisibility

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strict divisibility

(Definition)

Let and be elements of a commutative ring with non-zero unity and let $a \mid b$ . If there is a positive integer such that $a^n \mid b$ and $a^{n+1} \nmid b$ , then is strictly divisible by ; this may be denoted by

$\displaystyle a^n \parallel b.$

For example, $10^4 \parallel 520000$ .

Note. The expression “strictly divisible” may be used of course in a divisor monoid, too.

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"strict divisibility" is owned by pahio.

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Other names:

strictly divides

Also defines:

strictly divisible

Keywords:

divisible

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Cross-references: monoid, divisor, expression, integer, positive, non-zero unity, commutative ring
There are 2 references to this entry.

This is version 5 of strict divisibility, born on 2007-09-04, modified 2008-05-16.
Object id is 9916, canonical name is StrictDivisibility.
Accessed 460 times total.

Classification:

AMS MSC:	11A51 (Number theory :: Elementary number theory :: Factorization; primality)
	13A05 (Commutative rings and algebras :: General commutative ring theory :: Divisibility)

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