query: Non-principal ideal in $K[x,y]$?
positive_passages.docid: 20296
positive_passages.text: The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
negative_passages.docid: 87382
negative_passages.text: Non-invertible elements form an ideal
negative_passages.docid: 60223
negative_passages.text: Two principal ideals coincide if and only if their generators are associated
negative_passages.docid: 70249
negative_passages.text: Irreducibility of Polynomials in $k[x,y]$
negative_passages.docid: 127030
negative_passages.text: Simple example of non-arithmetic ring (non-distributive ideal lattice)
negative_passages.docid: 145507
negative_passages.text: Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
negative_passages.docid: 42652
negative_passages.text: Must $k$-subalgebra of $k[x]$ be finitely generated?
negative_passages.docid: 114640
negative_passages.text: Showing that an ideal is not a free $R-$module.
negative_passages.docid: 87780
negative_passages.text: Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
negative_passages.docid: 74537
negative_passages.text: Maximal Ideals in $K[y]$
negative_passages.docid: 147871
negative_passages.text: How do the prime ideals of $\mathbb{Z}_{k}$ look like?
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: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 144250
negative_passages.text: subideals of an ideal
negative_passages.docid: 129759
negative_passages.text: Must an ideal contain the kernel for its image to be an ideal?
negative_passages.docid: 156457
negative_passages.text: Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
negative_passages.docid: 9792
negative_passages.text: Is there an example of a power of prime ideal in a polynomial ring that is not primary?