Resumen de Self-injective Von Neumann regular subrings and a theorem of Pere Menal

Carl Faith

• This paper owes its origins to Pere Menal and his work on Von Neumann Regular (= VNR) rings, especially his work listed in the bibliography on when the tensor product K = A ÄK B of two algebras over a field k are right self-injective (= SI) or VNR. Pere showed that then A and B both enjoy the same property, SI or VNR, and furthermore that either A and B are algebraic algebras over k (see [M]). This is connected with a lemma in the proof of the Hilbert Nullstellensatz, namely a finite ring extension K = k[a1, ..., an] is a field only if a1, ..., an are algebraic over k.