query: Prime ideals of $M_{n,n}(R)$
positive_passages.docid: 19883
positive_passages.text: Prime ideals of the matrix ring
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: 93929
negative_passages.text: The height of a principal prime ideal
negative_passages.docid: 83050
negative_passages.text: Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
negative_passages.docid: 106550
negative_passages.text: The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$
negative_passages.docid: 16602
negative_passages.text: Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
negative_passages.docid: 146801
negative_passages.text: Primary decomposition of an ideal
negative_passages.docid: 105313
negative_passages.text: Existence of minimal prime ideal contained in given prime ideal and containing a given subset
negative_passages.docid: 73417
negative_passages.text: $Rad(I)$ is an ideal of $R$
negative_passages.docid: 60804
negative_passages.text: About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
negative_passages.docid: 141687
negative_passages.text: Nonprincipal prime ideals contain two relatively prime elements
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: 76813
negative_passages.text: The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
negative_passages.docid: 6699
negative_passages.text: An ideal that is maximal among non-finitely generated ideals is prime.
negative_passages.docid: 111287
negative_passages.text: number of prime ideals in algebraic integers
negative_passages.docid: 15904
negative_passages.text: Prime ideal and nilpotent elements
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