用对易子描述四元数

Mathematical Proceedings of the Royal Irish Academy Pub Date : 2021-07-21 DOI:10.1353/mpr.2022.0000

E. Kleinfeld, Yoav Segev

{"title":"用对易子描述四元数","authors":"E. Kleinfeld, Yoav Segev","doi":"10.1353/mpr.2022.0000","DOIUrl":null,"url":null,"abstract":"Abstract:Let R be an associative ring with 1, which is not commutative. Assume that any non-zero commutator v ∈ R satisfies: v2 is in the centre of R, and v is not a zero divisor.We prove that R has no zero divisors, and that if char(R) ≠ 2, then the localisation of R at its centre is a quaternion division algebra. Our proof is elementary and self contained.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"99 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A Characterisation of the Quaternions Using Commutators\",\"authors\":\"E. Kleinfeld, Yoav Segev\",\"doi\":\"10.1353/mpr.2022.0000\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract:Let R be an associative ring with 1, which is not commutative. Assume that any non-zero commutator v ∈ R satisfies: v2 is in the centre of R, and v is not a zero divisor.We prove that R has no zero divisors, and that if char(R) ≠ 2, then the localisation of R at its centre is a quaternion division algebra. Our proof is elementary and self contained.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"99 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1353/mpr.2022.0000\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1353/mpr.2022.0000","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

摘要:设R是一个不可交换的带1的结合环。设任意非零对易子v∈R满足:v2在R的中心，且v不是零因子。证明了R不存在零因子，且如果char(R)≠2，则R在其中心的定域是一个四元数除法代数。我们的证明是初等的和自成体系的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A Characterisation of the Quaternions Using Commutators

Abstract:

Let R be an associative ring with 1, which is not commutative. Assume that any non-zero commutator v ∈ R satisfies: v2 is in the centre of R, and v is not a zero divisor.

We prove that R has no zero divisors, and that if char(R) ≠ 2, then the localisation of R at its centre is a quaternion division algebra. Our proof is elementary and self contained.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Proceedings of the Royal Irish Academy

自引率

0.00%

发文量

期刊最新文献

Recent Advances In Exponential Random Graph Modelling Flux Limitation Mechanisms Arising in Multiscale Modelling of Cancer Invasion The Bergmann-Shilov boundary of a Bounded Symmetric Domain A Characterisation of the Quaternions Using Commutators Parallelogram Frameworks and Flexible Quasicrystals