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Difference between revisions of "Divisor (of an integer or of a polynomial)"

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A divisor of an integer $a$ is an integer $b$ which divides $a$ without remainder. In other words, a divisor of the integer $a$ is an integer $b$ such that, for a certain integer $c$, the equality $a=bc$ holds. A divisor of a polynomial $A(x)$ is a polynomial $B(x)$ that divides $A(x)$ without remainder (cf. [[Division|Division]]). More generally, in an arbitrary [[Ring|ring]] $A$, a divisor of an element $a \in A$ is an element $b\in A$ such that $a=bc$ for a certain $c\in A$.
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''For other meanings of the term 'Divisor' see the page'' [[Divisor (disambiguation)]]
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A divisor of an integer $a$ is an integer $b$ which divides $a$ without remainder. In other words, a divisor of the integer $a$ is an integer $b$ such that, for a certain integer $c$, the equality $a=bc$ holds.  
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A divisor of a polynomial $A(x)$ is a polynomial $B(x)$ that divides $A(x)$ without remainder (cf. [[Division|Division]]).  
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More generally, in an arbitrary [[Ring|ring]] $R$, a divisor of an element $a \in R$ is an element $b\in R$ such that $a=bc$ for a certain $c\in R$.
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If $b\in R$ is a divisor of $a\in R$, one writes $b | a$.

Revision as of 19:35, 20 October 2012


For other meanings of the term 'Divisor' see the page Divisor (disambiguation)

A divisor of an integer $a$ is an integer $b$ which divides $a$ without remainder. In other words, a divisor of the integer $a$ is an integer $b$ such that, for a certain integer $c$, the equality $a=bc$ holds.

A divisor of a polynomial $A(x)$ is a polynomial $B(x)$ that divides $A(x)$ without remainder (cf. Division).

More generally, in an arbitrary ring $R$, a divisor of an element $a \in R$ is an element $b\in R$ such that $a=bc$ for a certain $c\in R$.

If $b\in R$ is a divisor of $a\in R$, one writes $b | a$.

How to Cite This Entry:
Divisor (of an integer or of a polynomial). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Divisor_(of_an_integer_or_of_a_polynomial)&oldid=28578
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article