韦伯的《代数》与克罗内克的《Vorlesungen》：异同

IF 0.4 3区哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE

Historia Mathematica Pub Date : 2025-09-01 DOI:10.1016/j.hm.2025.07.003

Cédric Vergnerie

{"title":"韦伯的《代数》与克罗内克的《Vorlesungen》：异同","authors":"Cédric Vergnerie","doi":"10.1016/j.hm.2025.07.003","DOIUrl":null,"url":null,"abstract":"<div><div>The 19<sup>th</sup> century witnessed significant developments in the field of algebra, particularly in the theory of equations, which will be the focus of this examination. The contributions of Heinrich Weber and Leopold Kronecker to this area are especially noteworthy. To explore this, the article undertakes a comparative analysis of both the structure and content of Weber's <em>Lehrbuch der Algebra</em> and Kronecker's <em>Vorlesungen über die Theorie der algebraischen Gleichungen</em>. I will then attempt to show how this study allows us to gain insight into their respective conceptions of mathematics.</div></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":"72 ","pages":"Pages 8-38"},"PeriodicalIF":0.4000,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weber's Lehrbuch der Algebra and Kronecker's Vorlesungen: Similarities and differences\",\"authors\":\"Cédric Vergnerie\",\"doi\":\"10.1016/j.hm.2025.07.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The 19<sup>th</sup> century witnessed significant developments in the field of algebra, particularly in the theory of equations, which will be the focus of this examination. The contributions of Heinrich Weber and Leopold Kronecker to this area are especially noteworthy. To explore this, the article undertakes a comparative analysis of both the structure and content of Weber's <em>Lehrbuch der Algebra</em> and Kronecker's <em>Vorlesungen über die Theorie der algebraischen Gleichungen</em>. I will then attempt to show how this study allows us to gain insight into their respective conceptions of mathematics.</div></div>\",\"PeriodicalId\":51061,\"journal\":{\"name\":\"Historia Mathematica\",\"volume\":\"72 \",\"pages\":\"Pages 8-38\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2025-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Historia Mathematica\",\"FirstCategoryId\":\"98\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0315086025000412\",\"RegionNum\":3,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"HISTORY & PHILOSOPHY OF SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Historia Mathematica","FirstCategoryId":"98","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0315086025000412","RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}

引用次数: 0

摘要

19世纪见证了代数领域的重大发展，特别是在方程理论方面，这将是本次考试的重点。海因里希·韦伯和利奥波德·克罗内克对这一领域的贡献尤其值得注意。为了探讨这一点，本文对韦伯的《列尔布奇代数》和克罗内克的《代数理论》的结构和内容进行了比较分析。然后，我将尝试展示这项研究如何让我们深入了解他们各自的数学概念。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Weber's Lehrbuch der Algebra and Kronecker's Vorlesungen: Similarities and differences

The 19^th century witnessed significant developments in the field of algebra, particularly in the theory of equations, which will be the focus of this examination. The contributions of Heinrich Weber and Leopold Kronecker to this area are especially noteworthy. To explore this, the article undertakes a comparative analysis of both the structure and content of Weber's Lehrbuch der Algebra and Kronecker's Vorlesungen über die Theorie der algebraischen Gleichungen. I will then attempt to show how this study allows us to gain insight into their respective conceptions of mathematics.

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

Historia Mathematica 数学-科学史与科学哲学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

72 days

期刊介绍： Historia Mathematica publishes historical scholarship on mathematics and its development in all cultures and time periods. In particular, the journal encourages informed studies on mathematicians and their work in historical context, on the histories of institutions and organizations supportive of the mathematical endeavor, on historiographical topics in the history of mathematics, and on the interrelations between mathematical ideas, science, and the broader culture.