A Note on the (Faith-Menal) Counter Example

Abstract

Faith-Menal counter example is an example (unique) of a right John’s ring which is not right artinian In this paper we show that the ring T which considered as an example of a right Johns ring in the (Faith-Menal) Counter Example is also artinian. The conclusion is that the unique counter example that says a right John’s ring can not be right artinian is false and the right noetherian ring with the annihilator property rl(A) = A may be artinian.