On weak normality and symmetric algebras
type: Item
instance of: scholarly article
title: On weak normality and symmetric algebras
zbMATH Open document ID: 0534.13002
DOI: 10.1016/0021-8693(83)90117-5
author: Shiroh Itoh
published in: Journal of Algebra
publication date: 1983-01-01T00:00:00Z
review text: A symmetric R-algebra of rank one is by definition isomorphic to a symmetric algebra \(S_ R[L]\) where L is an invertible R-module, hence it is locally a polynomial algebra in one variable. In this paper the author proves that if \(R\subset S\) is a finite extension of reduced noetherian rings, then R is weakly normal in S if and only if every R-algebra A such that \(S\otimes_ RA\) is a symmetric algebra of rank one is itself a symmetric R-algebra of rank one. In the case where R is a field this is already well-known.
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 14C22
zbMATH DE Number: 3847530
zbMATH Keywords: weakly normal extension of noetherian rings
zbMATH Keywords: symmetric algebra
MaRDI profile type: Publication
full work available at URL: 0021-8693(83)90117-5
OpenAlex ID: W1995763809
cites work: Q5576163
cites work: On quasi-polynomial algebras
cites work: Locally polynomial algebras are symmetric algebras
cites work: Grothendieck groups and Picard groups of abelian group rings
cites work: Q4046174
cites work: Seminormality and projective modules over polynomial rings
cites work: Forms of the rings R[X] and R[X, Y]
cites work: Q5577247
cites work: Z-transforms and overrings of a Noetherian ring
cites work: Unipotent algebraic groups
cites work: Q5611879
cites work: Some remarks on polynomial rings
cites work: Some remarks on strongly invariant rings
cites work: Q4063564
cites work: Forms of the affine line and its additive group
cites work: On seminormality
cites work: Q5605674
cites work: Projective algebras
description: scientific article; zbMATH DE number 3847530