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Introduction to Modern Algebra and its Applications最新文献

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Polynomials in Several Variables 多元多项式
Introduction to Modern Algebra and its Applications Pub Date : 2021-06-08 DOI: 10.1201/9781003015482-8
N. Gubareni
{"title":"Polynomials in Several Variables","authors":"N. Gubareni","doi":"10.1201/9781003015482-8","DOIUrl":"https://doi.org/10.1201/9781003015482-8","url":null,"abstract":"On p 448 113, p 450 11, 110, p 451 117 add \"of measure one\" after \"extended unit monic polynomials\". On p 449 Z14-15 replace \"a hyperplane H containing C \" by \"a supporting hyperplane H of C with HCC = C On p 449 14, p 450 11, p 451 110 replace {2iv)n by (27r). On p 449 111 the expression (Z?=1 JM) should be in the exponent. On p 450 11 delete \"by Jensen's Theorem\". At the end of paper add: I would like to thank Prof. A. Schinzel and Dr. A. Bazylewicz for pointing out some errors in a preprint of this paper. Since submitting the paper I have found out that Lawton (J. Sci. Fac. Chaing Mai Univ. Thailand 4, 15-23 (1977)) outlined a proof of Cor. 1 using methods similar to those used here.","PeriodicalId":186933,"journal":{"name":"Introduction to Modern Algebra and its Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115610121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Elements of Field Theory 场论要素
Introduction to Modern Algebra and its Applications Pub Date : 2021-06-08 DOI: 10.1201/9781003015482-6
N. Gubareni
{"title":"Elements of Field Theory","authors":"N. Gubareni","doi":"10.1201/9781003015482-6","DOIUrl":"https://doi.org/10.1201/9781003015482-6","url":null,"abstract":"","PeriodicalId":186933,"journal":{"name":"Introduction to Modern Algebra and its Applications","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123250914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Examples of Applications 应用例子
Introduction to Modern Algebra and its Applications Pub Date : 2021-06-08 DOI: 10.1007/3-540-26403-5_14
N. Gubareni
{"title":"Examples of Applications","authors":"N. Gubareni","doi":"10.1007/3-540-26403-5_14","DOIUrl":"https://doi.org/10.1007/3-540-26403-5_14","url":null,"abstract":"","PeriodicalId":186933,"journal":{"name":"Introduction to Modern Algebra and its Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130567982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite Fields and their Applications 有限域及其应用
Introduction to Modern Algebra and its Applications Pub Date : 2021-06-08 DOI: 10.1201/9781003015482-9
N. Gubareni
{"title":"Finite Fields and their Applications","authors":"N. Gubareni","doi":"10.1201/9781003015482-9","DOIUrl":"https://doi.org/10.1201/9781003015482-9","url":null,"abstract":"We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields. Certain basic notions in finite field theory have interpretations in terms of standard graph properties. We show that the graphs are connected and provide an estimate of their diameter. An accidental graph isomorphism is uncovered and proved. The smallest non-trivial Laplace eigenvalue is given some attention, in particular for a specific family of 8-regular graphs showing that it is not an expander. We introduce a regular covering graph and show that it is connected if and only if the root is primitive. © 2020 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).","PeriodicalId":186933,"journal":{"name":"Introduction to Modern Algebra and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121833479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Elements of Number Theory 数论要素
Introduction to Modern Algebra and its Applications Pub Date : 2021-06-08 DOI: 10.1201/9781003015482-1
N. Gubareni
{"title":"Elements of Number Theory","authors":"N. Gubareni","doi":"10.1201/9781003015482-1","DOIUrl":"https://doi.org/10.1201/9781003015482-1","url":null,"abstract":"","PeriodicalId":186933,"journal":{"name":"Introduction to Modern Algebra and its Applications","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121851573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite Dimensional Algebras 有限维代数
Introduction to Modern Algebra and its Applications Pub Date : 2021-06-08 DOI: 10.1201/9781003015482-10
N. Gubareni
{"title":"Finite Dimensional Algebras","authors":"N. Gubareni","doi":"10.1201/9781003015482-10","DOIUrl":"https://doi.org/10.1201/9781003015482-10","url":null,"abstract":"","PeriodicalId":186933,"journal":{"name":"Introduction to Modern Algebra and its Applications","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127363977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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