Generalized quaternion algebras
type: Item
instance of: scholarly article
title: Generalized quaternion algebras
zbMATH Open document ID: 0841.16025
DOI: 10.1007/BF01208551
published in: Mathematical Notes
publication date: 1994-07-13T00:00:00Z
review text: Es sei \(A\) ein kommutativer Ring, in dem 2 invertierbar ist. Zu invertierbaren Elementen \(a,b\in A\) sei \(Q=(a,b/A)\) die verallgemeinerte Quaternionenalgebra. Der Verf. zeigt, daß \(Q\) genau dann rechtsdistributiv ist, wenn \(A\) distributiv und die quadratische Form \(x^2-ay^2-bz^2\) nullteilig modulo jedem maximalen Ideal \(M\) von \(A\) ist. Ist \(Q=(-1,-1/A)\) rechtsdistributiv, so ist \(1/2\in A\).
Mathematics Subject Classification ID: 16K20
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 11E99
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 589621
zbMATH Keywords: generalized quaternion algebras
zbMATH Keywords: quadratic forms
zbMATH Keywords: right distributive rings
author: A. A. Tuganbaev
reviewed by: Karl Mathiak
MaRDI profile type: Publication
cites work: Q5648449
cites work: Q3474808
full work available at URL: https://doi.org/10.1007/bf01208551
OpenAlex ID: W2070235674
description: scientific article; zbMATH DE number 589621