query: Every field has exactly 2 ideals
positive_passages.docid: 3129
positive_passages.text: A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
negative_passages.docid: 21604
negative_passages.text: A complete ring with respect to an ideal
negative_passages.docid: 147671
negative_passages.text: Find all ideals of $\mathbb R[x] / \langle x^2-3x+2\rangle$
negative_passages.docid: 29019
negative_passages.text: Ideals in direct product of rings
negative_passages.docid: 58640
negative_passages.text: $R$ is an algebra over an infinite field. If $\exists$ ideals s.t. $J\subseteq \bigcup_{k=1}^nI_k$ then $J\subseteq I_k$ for some $k$
negative_passages.docid: 146801
negative_passages.text: Primary decomposition of an ideal
negative_passages.docid: 69649
negative_passages.text: If an ideal contains the multiplicative identity, then it is the whole ring
negative_passages.docid: 94174
negative_passages.text: Ring of polynomials over a field has infinitely many primes
negative_passages.docid: 111114
negative_passages.text: Prove that an ideal in $k[x,y]$ is a prime ideal
negative_passages.docid: 50445
negative_passages.text: Explaining the product of two ideals
negative_passages.docid: 102341
negative_passages.text: Primary decomposition of a monomial ideal
negative_passages.docid: 33245
negative_passages.text: Show that every ideal of the ring $\mathbb Z$ is principal
negative_passages.docid: 74537
negative_passages.text: Maximal Ideals in $K[y]$
negative_passages.docid: 60391
negative_passages.text: Ideal Generated by Three Elements in Polynomial Ring
negative_passages.docid: 138672
negative_passages.text: Finding Ideals in $\begin{bmatrix} \mathbb{Q} & \mathbb{Q}\\ 0 & 0 \end{bmatrix}$
negative_passages.docid: 118513
negative_passages.text: Ideal of product of affine varieties
negative_passages.docid: 144250
negative_passages.text: subideals of an ideal