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...

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...

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...

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...

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...

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...

MR 0071721. Jacobson–Bourbaki theorem Jacobson's conjecture Jacobson density theorem Jacobson radical Jacobson ring "Nathan Jacobson (1910-1999)" (PDF)...

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...

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...

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...