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

Faith, Carl. "Self-injective Von Neumann regular subrings and a theorem of Pere Menal.." Publicacions Matemàtiques 36.2A (1992): 541-567. <http://eudml.org/doc/41734>.

@article{Faith1992,
abstract = {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 ⊗K 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.},
author = {Faith, Carl},
journal = {Publicacions Matemàtiques},
keywords = {right self-injective ring; von Neumann regular subrings; tensor product; right SI split-flat algebras; centralizing extension; maximal right quotient ring; central idempotents},
language = {eng},
number = {2A},
pages = {541-567},
title = {Self-injective Von Neumann regular subrings and a theorem of Pere Menal.},
url = {http://eudml.org/doc/41734},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Faith, Carl
TI - Self-injective Von Neumann regular subrings and a theorem of Pere Menal.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2A
SP - 541
EP - 567
AB - 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 ⊗K 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.
LA - eng
KW - right self-injective ring; von Neumann regular subrings; tensor product; right SI split-flat algebras; centralizing extension; maximal right quotient ring; central idempotents
UR - http://eudml.org/doc/41734
ER -