query: Is $M_a=\{f:f(a)=0\}$ a Principal ideal
positive_passages.docid: 135511
positive_passages.text: $M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$
negative_passages.docid: 43103
negative_passages.text: Unique factorization domain and principal ideals
negative_passages.docid: 109691
negative_passages.text: When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
negative_passages.docid: 31585
negative_passages.text: Primary ideals of $\mathbb{Z}$
negative_passages.docid: 464
negative_passages.text: Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
negative_passages.docid: 94157
negative_passages.text: Normal Ring and Prime Ideal whose Square is Principal
negative_passages.docid: 67342
negative_passages.text: Why does a minimal prime ideal consist of zerodivisors?
negative_passages.docid: 84663
negative_passages.text: $A$ local Noetherian ring with principal maximal ideal implies PIR?
negative_passages.docid: 80397
negative_passages.text: Show that this set of polynomials is ideal in F[x]
negative_passages.docid: 139334
negative_passages.text: Determining the existence or non-existence of Non Trivial Ideals of $L(V)$
negative_passages.docid: 89782
negative_passages.text: To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field
negative_passages.docid: 50908
negative_passages.text: Showing a Ring and an Ideal are equal
negative_passages.docid: 122189
negative_passages.text: Show that $M[x]$ is a Noetherian $A[x]$-module.
negative_passages.docid: 126672
negative_passages.text: Product of principal ideals: $(a)\cdot (b) = (a b)$
negative_passages.docid: 118306
negative_passages.text: $I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
negative_passages.docid: 53367
negative_passages.text: In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?