query: Radical of a Lie algebra is a characteristic ideal
positive_passages.docid: 153426
positive_passages.text: Is the radical of a Lie algebra preserved by all of its derivations?
negative_passages.docid: 15320
negative_passages.text: Morita equivalence and right and left ideals of a Ring
negative_passages.docid: 68065
negative_passages.text: Quadratic extensions in characteristic $2$
negative_passages.docid: 73417
negative_passages.text: $Rad(I)$ is an ideal of $R$
negative_passages.docid: 49854
negative_passages.text: Ideals in polynomial rings generated by linear polynomials
negative_passages.docid: 79650
negative_passages.text: Division Rings and Division Algebras
negative_passages.docid: 7833
negative_passages.text: Ideal and minimal polynomial
negative_passages.docid: 13371
negative_passages.text: Show that the Lie algebra generated by x, y with relations $ad(x)^2(y) = ad(y)^5(x) = 0$ is infinite dimensional and construct a basis
negative_passages.docid: 50236
negative_passages.text: Solvable Lie algebra with codimension 1 ideal
negative_passages.docid: 146801
negative_passages.text: Primary decomposition of an ideal
negative_passages.docid: 69373
negative_passages.text: Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
negative_passages.docid: 137450
negative_passages.text: Two-sided ideal generated by subset of not commutative ring
negative_passages.docid: 84677
negative_passages.text: An Explicit Isomorphism Between the Three Dimensional Orthogonal Lie Algebra and the Special Linear Lie Algebra of Dimension $3$
negative_passages.docid: 18406
negative_passages.text: An ideal whose radical is maximal is primary
negative_passages.docid: 123595
negative_passages.text: Representations of Direct Sum of Lie Algebras
negative_passages.docid: 11375
negative_passages.text: Jacobson radical of a certain ring of matrices
negative_passages.docid: 116883
negative_passages.text: About ideals in a ring which is a $k$ vector space