| In this paper the following result is obtained:(*): If Г-ring A satisfies ascending chain condition on left zero divisor ideals, then every strongly nil right ideal is strongly nilpotent.In order that (*) may contain the corresponding result of associative rings, a new concept, generalized Г-ring is introduced. So that any associative ring is naturally explained as a generalized Г-ring. It is proved that (*) is valid in the generalized Г-rings, thence the result of associative rings is a special case in the generalized Г-rings. |
