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

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 2A, page 541-567
- ISSN: 0214-1493

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topFaith, 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 -

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