由U-半单的亚直不可约环所确定的上根

THE UPPER RADICAL DETERMINED BY THE CLASS OF ALL U-SEMISIMPLE SUBDIRECTLYIRREDUCIBLE RINGS

F.A.Szazs在文献 [1 ]中提出了一个公开问题 ( problem42 ) :研究由所有没有非零诣零根的亚直不可约环所确定的上根 .在这篇文章中 ,我们解决了这个问题 .证明了这个根是一个特殊根 ,并证明了它严格包含 Bear上诣零根和反单根 .

F. A. Szasz has put forward a open problem(problem 42):Investigate the uper radical determined by the class of all subdirectly irreducible rings without non-zero nil radical. In this paper, the problem has been proved that the upper radicalr determined by the class of all subbirectly irreducible rings without non-zero nil radical is a special radical. Which contain strictly Bear upper nil radical U and antisimple radical.