query: Ring in which Jacobson Radical is different from nil radical
positive_passages.docid: 18003
positive_passages.text: Standard example where Jacobson radical not equal nilradical
negative_passages.docid: 5084
negative_passages.text: When is the completion of a ring a local ring ?
negative_passages.docid: 63192
negative_passages.text: A chain ring with Krull dimension greater than one
negative_passages.docid: 46843
negative_passages.text: A ring without the Invariant Basis Number property
negative_passages.docid: 157863
negative_passages.text: A finite pseudo-ring such that $ab^2=b$ for some $(a,b)\in A$
negative_passages.docid: 28327
negative_passages.text: (Simple) Examples on Non-Commutative Rings
negative_passages.docid: 77820
negative_passages.text: Roots in a polynomial ring
negative_passages.docid: 14191
negative_passages.text: How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the structure of this ring.
negative_passages.docid: 133019
negative_passages.text: Nilpotent elements in $\mathbb Z_n$
negative_passages.docid: 15904
negative_passages.text: Prime ideal and nilpotent elements
negative_passages.docid: 61292
negative_passages.text: How to know which elements are in the Quotient Ring $\mathbb{Z}[x]/\langle x, 2\rangle$?
negative_passages.docid: 157585
negative_passages.text: Structure theorem of finite rings
negative_passages.docid: 98818
negative_passages.text: Quotient ring of a localization of a ring
negative_passages.docid: 150206
negative_passages.text: Every finitely generated algebra over a field is a Jacobson ring
negative_passages.docid: 121255
negative_passages.text: Ideals of the ring of rational numbers with odd denominators
negative_passages.docid: 129025
negative_passages.text: Quotient ring local if Ring is local
negative_passages.docid: 83115
negative_passages.text: A set of elements in a reduced unity ring