中间超素环和中间超素根(英文)

The middle superprime rings and middle superprime radical

一个环R中的非零元a被称为一个中间零因子,如果存在R的非零元x和y,使得xay=0.一个环R称为中间超素环,如果它的每个非零理想都包含一个非零元素,它不是中间零因子.给出了一个环是中间超素环的一些等价条件,并证明了由所有的中间超素环组成的环类所确定的上根,即中间超素根,是一个特殊根.最后给出了中间超素根与常见的一些特殊根之间的关系.

An element a in ring R is called middle divisor of zero, if there exist non - zero elements x and y in R such that xay = 0. An ring R is said to be the middle superprime ring, if every non - zero ideal of R contains an non - zero element c, which is not middle divisor of zero. Some equivalent conditions that a ring is middle superprime ring are given, and it is shown that the upper radical determined by the class of the all middle superprime rings is a special radical. Lastly, the relationship between the middie superprime radical and usual special radicals is given.