关于DQrC-环

On Problems of DQrC Rings

中文关键词:  DQ_rC-环  K?the根  准质分解

英文关键词:DQ_rC ring,nil-radical,primary decompostion.

中文摘要:

      本文引进了DQ_rC-环.给出了DQ_rC-环的K?the根等于它的所有质理想交;右Noether DQ_rC-环每个理想皆可分解为有限个不可缩短右准质理想交，在稍强条件下，给出了Krull交定理在右Nocther DQ_rC-环上的推广.

英文摘要:

      We give the definition of DQ_rC ring，and prove that the nil-radical of R may be intersection of all the primary ideals. For a right Noether DQ_rC ring R，any nonideal of R may be decomposed into intersection of primary ideals of non-separated and generalize the Krull intersection theorem to the right Noether DQ_rC ring.