In ring theory, a branch of mathematics, semiprime ideals and semiprime rings are generalizations of prime ideals and prime rings. In commutative algebra...

generalized to non-commutative rings in the semiprime ring article. The radical of an ideal I {\displaystyle I} in a commutative ring R {\displaystyle R} , denoted...

I of a ring R is semiprime if for any ideal A of R, An ⊆ I implies A ⊆ I. Equivalently, I is semiprime if and only if R/I is a semiprime ring. semiprimitive...

or semiprime if for any a in R, if an is in I for some n, then a is in I. The factor ring of a radical ideal is a semiprime ring for general rings, and...

the semiprime right Goldie rings are precisely those that have a semisimple Artinian right classical ring of quotients. The structure of this ring of quotients...

ideals are prime, and prime ideals are both primary and semiprime. An ideal P of a commutative ring R is prime if it has the following two properties: If...

Primitive ring, Semiprimitive ring Prime ring, Semiprime ring, Reduced ring Integral domain, Domain (ring theory) Field of fractions, Integral closure Euclidean...

thirtieth semiprime, and the twenty-sixth distinct semiprime and the eighth of the form (3.q). together with 85 and 86, forms the last semiprime in the 2nd...

the semiprime right Goldie rings are precisely those that have a semisimple Artinian right classical ring of quotients. The structure of this ring of quotients...

determines the structure of primitive rings Goldie's theorem determines the structure of semiprime Goldie rings The Zariski–Samuel theorem determines...