根偶与某些正则根的补根

RADICALS PAIRS AND SUPPLEMENTING OF SOME REGULAR RADICALS

本文讨论在什么条件下(α∶β)是根环类的问题,在假定α为优(Superior)根的条件下分别得出(α∶β)为根类,为遗传根类的充要条件,作为应用具体地给出双正则根,强正则根的补根.

In this paper,we generalized the result of N.Divinsky and A.Sulinsky in[1].Let a is a superior radical,the necessary and sufficient condition for (α∶β)to be a radical,hereditary radical was obtained,respectively.The necessary andsufficient condition for (0∶β) to be a supplementing of radical β was given.Wealso discussed the supplementing of some regular radical.We point out thatthe supplementing of biregular radical,strongly regular radical was Brown-McCoy radical,Thierrin radical,respectively.