Noether环上加性秩函数对应的Gabriel拓扑与相应商环的构造

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

中文关键词:  Noether环  加性秩函数  Gabriel拓扑  商环

英文关键词:Noetherian rings  additive rank functions  Gabriel filters  quotient rings.

中文摘要:

      本文利用［１］中建立的关系，给出了半素右Ｎｏｅｔｈｃｒ环上所有加性秩函数对应的Ｇａｂｒｉｅｌ拓朴与相应商环的构造，并建立了一般Ｎｏｅｔｈｅｒ环上加性秩函数与Ａｒｔｉｎ环上模范畴中的有限长之间的联系．

英文摘要:

      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.