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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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* a divisor of an integer or polynomial or element of a ring; see [[divisor (of an integer)]];
 
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* a generalisation of the notion of divisor in a ring, or a divisor in algebraic geometry; see [[divisor(2)]];
 
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* the [[Poincaré divisor]] or theta divisor on a Jacobian.
 

Revision as of 18:27, 20 October 2012

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 $A$, a divisor of an element $a \in A$ is an element $b\in A$ such that $a=bc$ for a certain $c\in A$.

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=25208
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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