query: Nilradical strictly smaller than Jacobson radical.
positive_passages.docid: 18003
positive_passages.text: Standard example where Jacobson radical not equal nilradical
negative_passages.docid: 10585
negative_passages.text: Does a polynomial that's bounded below have a global minimum?
negative_passages.docid: 62232
negative_passages.text: A real $2 \times 2 $ matrix $M$ such that $M^2 = \tiny \begin{pmatrix} -1&0 \\ 0&-1-\epsilon \\ \end{pmatrix}$ , then :
negative_passages.docid: 1425
negative_passages.text: The Chinese Remainder Theorem for Rings.
negative_passages.docid: 6874
negative_passages.text: smallest value of $k$ for which $a_k$ is $0$
negative_passages.docid: 84382
negative_passages.text: Sole minimal element: Why not also the minimum?
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 155962
negative_passages.text: Are there irreducible polynomials that are partially solvable by radicals?
negative_passages.docid: 11375
negative_passages.text: Jacobson radical of a certain ring of matrices
negative_passages.docid: 35043
negative_passages.text: Cardinality of a set A is strictly less than the cardinality of the power set of A
negative_passages.docid: 118612
negative_passages.text: Neutral element in $\hom_C(A, B)$
negative_passages.docid: 123760
negative_passages.text: Smaller membership symbol
negative_passages.docid: 111935
negative_passages.text: Irreducible but not prime
negative_passages.docid: 63313
negative_passages.text: Uniqueness of Powerseries in an arbitrarily small neighborhood of $0$ in $\mathbb C$
negative_passages.docid: 53863
negative_passages.text: Making a non-diagonalizable matrix diagonalizable with an small perturbations
negative_passages.docid: 112666
negative_passages.text: Image of Jacobson Radical is the Jacobson Radical
negative_passages.docid: 129858
negative_passages.text: "Almost" ring homomorphism