根与右理想

Radicals and Right Ideals

给出根Ｒ分别满足：任意环的任意两个Ｒ－右理想之和仍为Ｒ－右理想，任意Ｒ－右理想升链之并仍为Ｂ－右理想，任意多个Ｒ－右理想之和仍为Ｒ－右理想的一些等价条件，并给出对任意环有最大Ｒ－右理想存在的古遗传根，亚强右遗传根，强右遗传根的元素刻划．

This note has given some equivalent condition for an radical properties R satisfy respectively the condition that the sum of two arbitrary R - right ideals in an arbitrary ring is again an R - right ideal,that the union of an arbitrary chain of R - right ideals an R - right ideal, that the sum of arbitrary R - right ideals an R - right ideal,and has given an element properties of right hereditary radicals that has the unique maximal R - right ideal in an arbitary ring, substrongyly right hereditary radicals, strongyly right hereditary radicals.