A Note on the (Faith-Menal) Counter Example

• 作者: R. H. Sallam
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: Johns RING ARTINIAN and NOETHERIAN RINGS
• 年，卷（期）: llsxjzyw_2012,（1）
• 页码范围: 39-40
• 页数: 2页
• 分类号: O1

摘要

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.