Difference between revisions of "Divisor (of an integer or of a polynomial)"
From Encyclopedia of Mathematics
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If $b\in R$ is a divisor of $a\in R$, one writes $b | a$. | If $b\in R$ is a divisor of $a\in R$, one writes $b | a$. | ||
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| + | If $a$ divides $b$ and $b$ divides $a$, then $a$ and $b$ are ''associates''. | ||
Revision as of 19:16, 22 November 2014
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 $b | a$.
If $a$ divides $b$ and $b$ divides $a$, then $a$ and $b$ are associates.
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=34824
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=34824
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article