The radical in alternative baric algebras
type: Item
instance of: scholarly article
title: The radical in alternative baric algebras
zbMATH Open document ID: 0968.17012
author: M. A. Couto
author: H. jun. Guzzo
published in: Archiv der Mathematik
publication date: 2001-09-16T00:00:00Z
review text: Let \(A\) be an algebra over a field \(F\), and \(\omega : A \rightarrow F\) a nonzero homomorphism. The ordered pair \((A, \omega\)) is called a baric algebra and \(\omega\) its weight. For \(B \subset A\) put \(\text{bar}(B)=\{x \in B : \omega(x)=0\}\). An algebra \(A\) is called an alternative algebra if \(x^2 y = x(xy)\), \(yx^2=(yx)x\), for all \(x, y \in A\). It is proved that in a baric, power associative, algebra over \(F\) of finite dimension, there is an idempotent element of weight 1. In the case when this algebra is alternative the Peirce's decomposition with this idempotent is considered. The nil radical as the maximal nil ideal is defined. It is proved that the bar-radical is the intersection of the nil radical with the square of \(\text{bar}(A)\).
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 17A65
Mathematics Subject Classification ID: 17D92
zbMATH DE Number: 1547965
zbMATH Keywords: baric algebras
zbMATH Keywords: alternative algebras
zbMATH Keywords: nil radical
zbMATH Keywords: nil ideal
reviewed by: A. A. Rakhimov
MaRDI profile type: Publication
full work available at URL: s000130050490
OpenAlex ID: W2047972802
DOI: 10.1007/S000130050490
description: scientific article; zbMATH DE number 1547965