【摘要】 <正> 本文讨论的环,概指结合环,环 R 说是一个 MHR 环,如果 R 对主右理想有极小条件。我们知道,对于 Artin 环来说,Jacobson 根与 Baer 根在强意下一致(见[1],7.1c),而 Jacobson 根与 Z 根(即一切平凡单环决定的下根)在弱意义下一致(见[1],引理[28],本文证明,上述结果对 MHR 环也成立,作为推论,给出[2]中问题37的肯定回答:每一个 MHR 诣零环是 Z 根环。更多还原

【Abstract】 By an MHR-ring,we mean a ring with minimum condition on right principalideals,Z be the lower radical determined by the class of all zero-rings ofprime number order.In this note,the following theorems are proved:1)Let J(R) be the Jacobson radical and B(R) the Baer radical (lowernil radical) of a ring R.Then or(R)=B(R) for every MHR-ring R.2)If R is MHR Jacobson radical ring,then R is Z radical ring.As a corollary,we give an affirmative answer of the problem 37 of F.A.Szasz:every MHR nil ring is Z radical ring.更多还原