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| − | ''of an integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336901.png" />'' | + | "'''Divisor'''" may refer to: |
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| − | An integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336902.png" /> which divides the number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336903.png" /> without remainder. In other words, a divisor of the integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336904.png" /> is an integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336905.png" /> such that, for a certain integer <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336906.png" />, the equality <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336907.png" /> holds. A divisor of a polynomial <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336908.png" /> is a polynomial <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d0336909.png" /> that divides <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369010.png" /> without remainder (cf. [[Division|Division]]). More generally, in an arbitrary ring <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369011.png" /> a divisor of an element <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369012.png" /> is an element <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369013.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369014.png" /> for a certain <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d033/d033690/d03369015.png" />.
| + | * a divisor of an integer or polynomial; see [[divisor (of an integer)]]; |
| | + | * a divisor in a more general ring, or in algebraic geometry; see [[divisor(2)]]. |
Revision as of 01:07, 24 April 2012
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=25206
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article