zero polynomial

The zero polynomialMathworldPlanetmath in a ring R[X] of polynomialsMathworldPlanetmathPlanetmathPlanetmath over a ring R is the identity elementMathworldPlanetmath 0 of this polynomial ring:


So the zero polynomial is also the absorbing element for the multiplication of polynomials.

All coefficients of the zero polynomial are equal to 0, i.e.

𝟎:=(0, 0, 0,).

Because always


and because in general  deg(fg)=deg(f)+deg(g)  when R has no zero divisorsMathworldPlanetmath, one may define that that the zero polynomial has no degree ( at all, or alternatively that


(see the extended real numbers).

Title zero polynomial
Canonical name ZeroPolynomial
Date of creation 2013-03-22 14:46:58
Last modified on 2013-03-22 14:46:58
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 13
Author pahio (2872)
Entry type Definition
Classification msc 13P05
Classification msc 11C08
Classification msc 12E05
Related topic PolynomialRingOverIntegralDomain
Related topic OrderAndDegreeOfPolynomial
Related topic MinimalPolynomialEndomorphism