分次环的分次素秩和分次反单根

研究对于具有某种性质的Ｇ－分次环Ｒ（Ｇ是有限群），当不考虑分次时，是否具有类似的性质．为此，首先证明了不相容性，即若是Ｒ＃Ｇ＊的两个理想且Ｐ是素的，则作为它的应用，证得分次环的分次素秩与素秩是相等的，其次，得到当时，Ｒ的分次反单根与反单根是一致的．

Graded Prime Ranks and Graded Antisimple Radicals of Rings Graded by Finite groups

Let R be graded by a finite group G. Our main purpose is to see whether a graded ring with a certain property has a similar property when regarded as being without grading. First, we prove the incomparability: Let P Q be ideals of R #G* with P being prime, then P R Q p. As its application, we show that the graded prime rank of R is equal to the prime rank of R. Then, we prove that if, then the graded antisimple radical of R is equal to the antisimple radical of R.