query: Ideals and quotient rings
positive_passages.docid: 36980
positive_passages.text: Prove the third isomorphism theorem
negative_passages.docid: 135699
negative_passages.text: Questions about a commutative ring with exactly three ideals
negative_passages.docid: 148550
negative_passages.text: Units in quotient ring of $\mathbb Z[X]$
negative_passages.docid: 74796
negative_passages.text: Extension of intersection of ideals
negative_passages.docid: 87078
negative_passages.text: Prove the following set is an ideal of the ring $Z[x]$
negative_passages.docid: 45684
negative_passages.text: Is quotient of a ring by a power of a maximal ideal local?
negative_passages.docid: 104377
negative_passages.text: Maximal Ideals in Ring of Continuous Functions
negative_passages.docid: 142863
negative_passages.text: Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
negative_passages.docid: 138672
negative_passages.text: Finding Ideals in $\begin{bmatrix} \mathbb{Q} & \mathbb{Q}\\ 0 & 0 \end{bmatrix}$
negative_passages.docid: 50445
negative_passages.text: Explaining the product of two ideals
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 19883
negative_passages.text: Prime ideals of the matrix ring
negative_passages.docid: 137450
negative_passages.text: Two-sided ideal generated by subset of not commutative ring
negative_passages.docid: 40678
negative_passages.text: Image of an ideal under a surjective ring homomorphism is an ideal
negative_passages.docid: 138114
negative_passages.text: Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
negative_passages.docid: 68167
negative_passages.text: Intersection of powers of an ideal in a Noetherian ring
negative_passages.docid: 41629
negative_passages.text: Structure of ideals in the product of two rings