The Construction of the Gabriel Topologies Arising from any Additive Rank Function and the Corresponding Quotient Rings for any Right Noetherian Semiprime Ring

Abstract:

      Using the corresponding relationship built by the method used in [1], we give the construction of the Gabriel topologies arising from any additive rank function and the con- struction of the corresponding quotient rings for any right noetherian semiprime ring. There- fore we establish the association between the additive rank function in noetherian rings and the finite length in the module category for an artinian ring.