TITLE:
A Note on the (Faith-Menal) Counter Example
AUTHORS:
R. H. Sallam
KEYWORDS:
Johns Ring; Artinian and Noetherian Rings
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.1,
January
6,
2012
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.