{"title":"关于Dedekind格的一些性质","authors":"K. Othman","doi":"10.54216/gjmsa.030102","DOIUrl":null,"url":null,"abstract":"The objective of this paper is to study the Dedekind lattices, where we prove if is a -lattice and domain, then will be a Dedekind domain if and only if every non zero maximal element is invertible. On the other hand, we prove that if is a domain and -lattices, then is a dedehind domain if and only if is a UFD lattices and every non zero prime element is maximal.","PeriodicalId":299243,"journal":{"name":"Galoitica: Journal of Mathematical Structures and Applications","volume":"115 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Some Properties of Dedekind Lattices\",\"authors\":\"K. Othman\",\"doi\":\"10.54216/gjmsa.030102\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The objective of this paper is to study the Dedekind lattices, where we prove if is a -lattice and domain, then will be a Dedekind domain if and only if every non zero maximal element is invertible. On the other hand, we prove that if is a domain and -lattices, then is a dedehind domain if and only if is a UFD lattices and every non zero prime element is maximal.\",\"PeriodicalId\":299243,\"journal\":{\"name\":\"Galoitica: Journal of Mathematical Structures and Applications\",\"volume\":\"115 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Galoitica: Journal of Mathematical Structures and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54216/gjmsa.030102\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Galoitica: Journal of Mathematical Structures and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54216/gjmsa.030102","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The objective of this paper is to study the Dedekind lattices, where we prove if is a -lattice and domain, then will be a Dedekind domain if and only if every non zero maximal element is invertible. On the other hand, we prove that if is a domain and -lattices, then is a dedehind domain if and only if is a UFD lattices and every non zero prime element is maximal.
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