Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou
{"title":"论强无相干环和强无非ether环","authors":"Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou","doi":"10.1007/s41980-023-00856-7","DOIUrl":null,"url":null,"abstract":"<p>The first part of this paper introduces and studies the class of strongly nonnil-coherent rings, a subclass of the already defined and studied class of nonnil-coherent rings. Contrary to the classical result that every Noetherian ring is coherent, a nonnil-Noetherian ring need not be nonnil-coherent. To remedy this, the second part introduces and studies the class of strongly nonnil-Noetherian rings, a subclass of the class of nonnil-Noetherian rings. Some examples are also given to illustrate the results.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Strongly Nonnil-Coherent Rings and Strongly Nonnil-Noetherian Rings\",\"authors\":\"Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou\",\"doi\":\"10.1007/s41980-023-00856-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The first part of this paper introduces and studies the class of strongly nonnil-coherent rings, a subclass of the already defined and studied class of nonnil-coherent rings. Contrary to the classical result that every Noetherian ring is coherent, a nonnil-Noetherian ring need not be nonnil-coherent. To remedy this, the second part introduces and studies the class of strongly nonnil-Noetherian rings, a subclass of the class of nonnil-Noetherian rings. Some examples are also given to illustrate the results.</p>\",\"PeriodicalId\":9395,\"journal\":{\"name\":\"Bulletin of The Iranian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-03-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Iranian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s41980-023-00856-7\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-023-00856-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Strongly Nonnil-Coherent Rings and Strongly Nonnil-Noetherian Rings
The first part of this paper introduces and studies the class of strongly nonnil-coherent rings, a subclass of the already defined and studied class of nonnil-coherent rings. Contrary to the classical result that every Noetherian ring is coherent, a nonnil-Noetherian ring need not be nonnil-coherent. To remedy this, the second part introduces and studies the class of strongly nonnil-Noetherian rings, a subclass of the class of nonnil-Noetherian rings. Some examples are also given to illustrate the results.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
