Let be a ring with an identity. Then has a right classical ring of quotients which is semisimple Artinian if and only if is a semiprime right Goldie ring. If this is the case, then the composition length of is equal to the uniform dimension of .
An immediate corollary of this is that a semiprime right Noetherian ring always has a right classical ring of quotients.
This result was discovered by Alfred in the late 1950’s.
|Date of creation||2013-03-22 14:04:17|
|Last modified on||2013-03-22 14:04:17|
|Last modified by||mclase (549)|