Alternative rings whose associators are not zero-divisors

Erwin Kleinfeld; Yoav Segev

doi:10.1007/s00013-021-01646-5

Alternative rings whose associators are not zero-divisors

Erwin Kleinfeld
, Yoav Segev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The purpose of this short note is to prove that if R is an alternative ring whose associators are not zero-divisors, then R has no zero-divisors. By a result of Bruck and Kleinfeld, if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field.

Original language	English
Pages (from-to)	613-616
Number of pages	4
Journal	Archiv der Mathematik
Volume	117
Issue number	6
DOIs	https://doi.org/10.1007/s00013-021-01646-5
State	Published - 1 Dec 2021

Keywords

Alternative ring
Associator
Commutator
Octonion algebra

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00013-021-01646-5

Cite this

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abstract = "The purpose of this short note is to prove that if R is an alternative ring whose associators are not zero-divisors, then R has no zero-divisors. By a result of Bruck and Kleinfeld, if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field.",

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KW - Associator

KW - Commutator

KW - Octonion algebra

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Alternative rings whose associators are not zero-divisors

Abstract

Keywords

ASJC Scopus subject areas

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