algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals. For commutative rings primitive ideals...
6 KB (829 words) - 15:16, 26 April 2024
In mathematics, more specifically ring theory, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple...
25 KB (2,879 words) - 15:59, 24 August 2024
following characterization of a Jacobson ring contains Zariski's lemma as a special case. Recall that a ring is a Jacobson ring if every prime ideal is an...
7 KB (1,259 words) - 10:45, 9 August 2024
ideal, the Jacobson radical — which is the intersection of maximal ideals — must contain the nilradical. A ring R is called a Jacobson ring if the nilradical...
7 KB (1,066 words) - 18:37, 12 August 2024
a semiprimitive ring or Jacobson semisimple ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more general than...
3 KB (372 words) - 18:27, 14 June 2022
contain I. This says that R is a Jacobson ring. The Baer radical of a ring is the intersection of the prime ideals of the ring R. Equivalently it is the smallest...
11 KB (1,362 words) - 01:24, 28 March 2024
MR 0071721. Jacobson–Bourbaki theorem Jacobson's conjecture Jacobson density theorem Jacobson radical Jacobson ring "Nathan Jacobson (1910-1999)" (PDF)...
13 KB (1,194 words) - 11:32, 18 July 2024
non-commutative ring theory, modern algebra, and module theory, the Jacobson density theorem is a theorem concerning simple modules over a ring R. The theorem...
9 KB (1,139 words) - 16:47, 22 August 2023
R=k[t_{1},\cdots ,t_{n}]/I} ) is Jacobson. More generally, one has the following theorem: Let R {\displaystyle R} be a Jacobson ring. If S {\displaystyle S} is...
23 KB (3,796 words) - 17:48, 18 August 2024
ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more general than a semisimple ring, but where simple modules...
20 KB (2,804 words) - 01:41, 1 November 2023