Abstract
The purpose of this note is to provide examples of simple, right and left self-injective rings which are not artinian, thus contradicting a theorem of S. Elliger [“On simple injective rings”, Proc. Amer. Math. Soc. 40 (1973), 93-94]. These examples also answer (negatively) a question of the author regarding the structure of prime, regular, right self-injective rings
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