query: Give an example of a ring in which an ideal of an ideal is not an ideal
positive_passages.docid: 144250
positive_passages.text: subideals of an ideal
negative_passages.docid: 54916
negative_passages.text: Maximal ideal in commutative ring
negative_passages.docid: 11573
negative_passages.text: Rings and some of their properties
negative_passages.docid: 149136
negative_passages.text: On the height of an ideal
negative_passages.docid: 86816
negative_passages.text: Example of two prime ideals whose intersection of the squares not equal to the square of the intersection
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 4507
negative_passages.text: Localization of a ring which is not a domain
negative_passages.docid: 104486
negative_passages.text: Ideal in $\mathbb Z[x]$ which is not two-generated
negative_passages.docid: 87078
negative_passages.text: Prove the following set is an ideal of the ring $Z[x]$
negative_passages.docid: 127030
negative_passages.text: Simple example of non-arithmetic ring (non-distributive ideal lattice)
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.
negative_passages.docid: 28327
negative_passages.text: (Simple) Examples on Non-Commutative Rings
negative_passages.docid: 21604
negative_passages.text: A complete ring with respect to an ideal
negative_passages.docid: 157863
negative_passages.text: A finite pseudo-ring such that $ab^2=b$ for some $(a,b)\in A$
negative_passages.docid: 117590
negative_passages.text: Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
negative_passages.docid: 77112
negative_passages.text: Artinian rings that are not Artin algebras