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

• Autores: Carl Faith
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 2, 1, 1992 (Ejemplar dedicado a: la memória de Pere Menal i Brufal), págs. 541-567
• Idioma: inglés
• DOI: 10.5565/publmat_362a92_17
• Títulos paralelos:
  • Subanillos regulares de Von Neumann autoinyectivos y un teorema de Pere Menal
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• Resumen

  • 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.