{"title":"Some Special Refined Neutrosophic Ideals in Refined Neutrosophic Rings: A Proof-of-Concept Study","authors":"Murhaf Riad Alabdullah","doi":"10.61356/j.nswa.2024.96","DOIUrl":null,"url":null,"abstract":"In this research, we created notions of a refined neutrosophic prime (completely prime, semiprime, and completely semiprime) ideal in a refined neutrosophic ring. If R(I1, I2) is a refined neutrosophic ring, then each ideal of R(I1, I2) has the form J+KI1+LI2 are ideals of the classical ring R. The objective of this work is to find the necessary and sufficient condition on classical ideals J, L and K that makes J+KI1+LI2 a prime (completely prime, semiprime, and completely semiprime) ideal in R(I1, I2). We studied some of the elementary properties of these concepts and the most important properties that link them. ","PeriodicalId":169974,"journal":{"name":"Neutrosophic Systems with Applications","volume":"83 11","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neutrosophic Systems with Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.61356/j.nswa.2024.96","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this research, we created notions of a refined neutrosophic prime (completely prime, semiprime, and completely semiprime) ideal in a refined neutrosophic ring. If R(I1, I2) is a refined neutrosophic ring, then each ideal of R(I1, I2) has the form J+KI1+LI2 are ideals of the classical ring R. The objective of this work is to find the necessary and sufficient condition on classical ideals J, L and K that makes J+KI1+LI2 a prime (completely prime, semiprime, and completely semiprime) ideal in R(I1, I2). We studied some of the elementary properties of these concepts and the most important properties that link them.
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