Is it possible to define a zero $f(x)$ in a ring $R[x]$ of polynomials as a display of the form: $(\forall x \in R)$ $f(x)=0$ ?
Asked
Active
Viewed 316 times
1 Answers
0
For $R=\mathbb{F}_5$, for example, take $f=X(X-1)(X-2)(X-3)(X-4)$. Then, as a polynomial, $f\neq0$ but $f(x)=0$ for all $x\in R$.
RMWGNE96
- 801
-
Isn't this polynomial a zero element in a given polynomial ring? – MorrisonFJ May 29 '19 at 11:45
-
1@MorrisonFJ No, it is not the zeor polynomial (the zero element in $R$), because its degree as a polynomial is $5$. – Dietrich Burde May 29 '19 at 11:51