query: Why is $[\mathfrak{q}, \mathfrak{g}]$ the smallest ideal $\mathfrak{a}$ of $\mathfrak{g}$ such that $\mathfrak{g}/\mathfrak{a}$ is reductive.
positive_passages.docid: 20479
positive_passages.text: Radical of a Lie algebra bracket itself
negative_passages.docid: 116430
negative_passages.text: If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
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: 91627
negative_passages.text: What is a primary decomposition of the ideal $I = \langle xy, x - yz \rangle$?
negative_passages.docid: 34807
negative_passages.text: Localization at finitely many minimal prime ideals
negative_passages.docid: 73689
negative_passages.text: A question about the equivalence relation on the localization of a ring.
negative_passages.docid: 16945
negative_passages.text: Finding the Ideals of a Direct Product of Rings
negative_passages.docid: 125888
negative_passages.text: Nilradical strictly smaller than Jacobson radical.
negative_passages.docid: 138572
negative_passages.text: Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 146714
negative_passages.text: Rees algebra of a monomial ideal
negative_passages.docid: 103518
negative_passages.text: If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
negative_passages.docid: 50908
negative_passages.text: Showing a Ring and an Ideal are equal
negative_passages.docid: 124646
negative_passages.text: Understanding the ideal $IJ$ in $R$
negative_passages.docid: 68202
negative_passages.text: Must an ideal generated by an irreducible element be a maximal ideal?
negative_passages.docid: 75039
negative_passages.text: Smallest positive element of $ \{ax + by: x,y \in \mathbb{Z}\}$ is $\gcd(a,b)$
negative_passages.docid: 13901
negative_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$