一致环的半素性

The semiprime qualities of uniform rings

讨论了一致环的半素性,证明了:(1)设J是有非零零因子约化环R的一个一致左理想,则对任意0≠a∈J,都有r(J)=r(a);(2)半素左一致DQC环是无零因子环;(3)半素左一致左P-内射环是体。

Semiprime quality of uniform rings is discussed. It is shown that： （ 1 ） Suppose that J is a left uniform ideal ofareduced ring R who has no zero-factor except zero, then r（J） =r（a） for any0≠α∈J; （2） A semiprime left uniform and DQC ring is certain a non zero - divisor ring ; and （3） A semiprime left uniform and left P- injective ring is certain a divisor ring.