关于一类环确定的上根

On the upper radical determined by a class of rings.

对环类Ｍ，用ＵＭ表示由Ｍ所确定的上根．若Ｍ中环都是有单位元的单环，则（ａ）ＵＭ是遗传根；（ｂ）对任意环Ｒ，ＵＭ（Ｒ）＝∩｛Ｉ：ＩＲ，Ｒ／Ｉ∈Ｍ｝．讨论了由亚直既约环类所确定的上根。

The author give certain sufficient or necessary conditions on a class M of subdirectly irreducible rings for UM satisfies property (Int).For wantonly rings R UM(R)=∩{I:IR,R/I∈M} . Some results are generalized.