On Noetherian rings with essential socle

Abstract

It is shown that if R is a right Noetherian ring whose right socle is essential as a right ideal and is contained in the left socle, then R is right Artinian. This result may be viewed as a one-sided version of a result of Ginn and Moss on two-sided Noetherian rings with essential socle. This also extends the work of Nicholson and Yousif where the same result is obtained under a stronger hypothesis. We use our work to obtain partial positive answers to some open questions on right CF, right FGF and right Johns rings.