{"title":"线性右理想近环的一些性质","authors":"K. D. Magill","doi":"10.1155/S0161171203306295","DOIUrl":null,"url":null,"abstract":"In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"4085-4113"},"PeriodicalIF":1.0000,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203306295","citationCount":"0","resultStr":"{\"title\":\"Some properties of linear right ideal nearrings\",\"authors\":\"K. D. Magill\",\"doi\":\"10.1155/S0161171203306295\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$\\\" xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.\",\"PeriodicalId\":39893,\"journal\":{\"name\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"volume\":\"2003 1\",\"pages\":\"4085-4113\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2003-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/S0161171203306295\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/S0161171203306295\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/S0161171203306295","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
在之前的纸,我们确定所有这些拓扑nearrings𝒩n的添加剂组n维欧氏集团,1美元“xmlns: mml = " http://www.w3.org/1998/Math/MathML " > n > 1,和含有n维线性子空间我}{J = 1 n也对附近的理想的属性为每个w∈𝒩n,存在w我∈J, 1≤≤n,这样w = w w 1 + 2 +⋯+ w n和v w = w n为每个v∈𝒩n。在本文中,我们确定了这些近环的性质,它们的理想,当其中两个近环同构时,我们研究了这些近环的乘法半群。
In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.
期刊介绍:
The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.