{"title":"PRIMENESS AND PRIMITIVITY IN NEAR-RINGS","authors":"G. Wendt","doi":"10.4134/JKMS.J200013","DOIUrl":null,"url":null,"abstract":"In near-ring theory several different types of primitivity exist. These all imply several different types of primeness. In case of near-rings with DCCN most of the types of primeness are known to imply primitivity of a certain kind. We are able to show that also so called 1-prime nearrings imply 1-primitivity. This enables us to classify maximal ideals in near-rings with chain condition with the concept of 1-primeness which leads to further results in the structure theory of near-rings.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"58 1","pages":"309-326"},"PeriodicalIF":0.7000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J200013","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In near-ring theory several different types of primitivity exist. These all imply several different types of primeness. In case of near-rings with DCCN most of the types of primeness are known to imply primitivity of a certain kind. We are able to show that also so called 1-prime nearrings imply 1-primitivity. This enables us to classify maximal ideals in near-rings with chain condition with the concept of 1-primeness which leads to further results in the structure theory of near-rings.
期刊介绍：
This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).
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