query: Let $A$ be a commutative ring and $f\in A[X]$ with $f \not\equiv 0$. Show that if $f|0$ in $A[X]$ then $\exists a \in A$ st $a \neq 0$ and $af = 0$
positive_passages.docid: 17926
positive_passages.text: Zero divisor in $R[x]$
negative_passages.docid: 30860
negative_passages.text: Prove that $f(x)=0$ in $[-1,1]$.
negative_passages.docid: 14055
negative_passages.text: How to show that a finite commutative ring without zero divisors is a field?
negative_passages.docid: 67291
negative_passages.text: Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
negative_passages.docid: 36996
negative_passages.text: If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
negative_passages.docid: 34908
negative_passages.text: $A$ is normal and nilpotent, show $A=0$
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 77198
negative_passages.text: Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
negative_passages.docid: 29126
negative_passages.text: Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
negative_passages.docid: 113512
negative_passages.text: Characteristic of nonzero commutative rings with unity
negative_passages.docid: 17895
negative_passages.text: Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
negative_passages.docid: 45602
negative_passages.text: Show that is $\int_A f$ exists, then so does $\int_A |f|$
negative_passages.docid: 69869
negative_passages.text: if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
negative_passages.docid: 111485
negative_passages.text: Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
negative_passages.docid: 50012
negative_passages.text: $f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
negative_passages.docid: 84313
negative_passages.text: $|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
negative_passages.docid: 80961
negative_passages.text: Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain