{"title":"REGULARITY AND IDEALS IN NEAR-SEMIRINGS","authors":"U. Leerawat, Benya Setthanarak","doi":"10.17654/0972555523003","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate conditions that force regular near-semirings (additive or multiplicative regular near-semirings) to be idempotent (additive idempotent). In addition, we study some kinds of ideals as p-ideals and subtractive ideals in near-semirings and investigate their properties in near-semirings. Finally, we define two congruence relations on a near-semiring, and an additive inverse regular near-semiring, respectively. Then we give constructions of quotient near-semirings induced by congruence relations.","PeriodicalId":43248,"journal":{"name":"JP Journal of Algebra Number Theory and Applications","volume":"14 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"JP Journal of Algebra Number Theory and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/0972555523003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate conditions that force regular near-semirings (additive or multiplicative regular near-semirings) to be idempotent (additive idempotent). In addition, we study some kinds of ideals as p-ideals and subtractive ideals in near-semirings and investigate their properties in near-semirings. Finally, we define two congruence relations on a near-semiring, and an additive inverse regular near-semiring, respectively. Then we give constructions of quotient near-semirings induced by congruence relations.
期刊介绍：
The JP Journal of Algebra, Number Theory and Applications is a peer-reviewed international journal. Original research papers theoretical, computational or applied, in nature, in any branch of Algebra and Number Theory are considered by the JPANTA. Together with the core topics in these fields along with their interplay, the journal promotes contributions in Diophantine equations, Representation theory, and Cryptography. Realising the need of wide range of information for any emerging area of potential research, the journal encourages the submission of related survey articles as well.
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