Self-duality and ring extensions
type: Item
instance of: scholarly article
title: Self-duality and ring extensions
zbMATH Open document ID: 0537.16018
DOI: 10.1016/0022-4049(84)90014-8
author: Takashi Mano
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: The author studies the relationship between ring extensions and self- duality. He generalizes a result of Fuller and Haack (a finite 'zR semigroup ring' over a ring with self-duality has itself a self-duality) in the following Theorem: Let \(A\supseteq B\) be a ring extension. If A has a finite free basis over B each member of which centralizes all the elements of B, B has a self-duality induced by \({}_ BV_ B\), and if the structure constants of A with respect to the above basis commute with each element of V, then A has a self-duality induced by \(_ AHom_ B(_ BA_ A,_ BV).\)
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16S20
zbMATH DE Number: 3853303
zbMATH Keywords: ring extensions
zbMATH Keywords: free basis
zbMATH Keywords: self-duality
reviewed by: T. W. Hungerford
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90014-8
OpenAlex ID: W2065902899
cites work: Duality for semigroup rings
cites work: Q3248050
cites work: Rings with Duality
Wikidata QID: Q127190565
description: scientific article; zbMATH DE number 3853303