query: Ideals of the real numbers
positive_passages.docid: 41629
positive_passages.text: Structure of ideals in the product of two rings
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: 89056
negative_passages.text: Intuitive understanding of ideal $I = (x+1,x^2+1)$ and the quotient $\Bbb Z[x]/I$
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
negative_passages.docid: 104486
negative_passages.text: Ideal in $\mathbb Z[x]$ which is not two-generated
negative_passages.docid: 139334
negative_passages.text: Determining the existence or non-existence of Non Trivial Ideals of $L(V)$
negative_passages.docid: 109688
negative_passages.text: Zero-dimensional ideals and finite-dimensional algebras
negative_passages.docid: 58425
negative_passages.text: Defining the Product of Ideals
negative_passages.docid: 27766
negative_passages.text: Comaximal ideals in a commutative ring
negative_passages.docid: 16945
negative_passages.text: Finding the Ideals of a Direct Product of Rings
negative_passages.docid: 75204
negative_passages.text: Irrationality $\sqrt{2}$ with ideal
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 157605
negative_passages.text: $IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$
negative_passages.docid: 102341
negative_passages.text: Primary decomposition of a monomial ideal
negative_passages.docid: 90889
negative_passages.text: Prime ideals in a finite direct product of rings
negative_passages.docid: 129302
negative_passages.text: Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 87078
negative_passages.text: Prove the following set is an ideal of the ring $Z[x]$