{"title":"伪环代数中的模糊理想","authors":"Teferi Getachew Alemayehu","doi":"10.1155/2022/4643252","DOIUrl":null,"url":null,"abstract":"In this study, fuzzy ideals in pseudo-hoop algebras are presented. Also, we investigate fuzzy congruences relations on pseudo-hoop algebras induced by fuzzy ideals. By using fuzzy ideals, we create the fuzzy quotient pseudo-hoop algebras and identify and demonstrate the one-to-one relationship between the set of all normal fuzzy ideals of a pseudo-hoop algebra \n \n H\n \n with conditions \n \n \n \n p\n \n D\n N\n \n \n \n and the set of all fuzzy congruences relation on \n \n H\n \n . Additionally, we investigate the relationship between fuzzy ideals and fuzzy filters in pseudo-hoop algebras by considering the set of complement elements of pseudo-hoop algebras. Lastly, we study fuzzy prime ideals and fuzzy \n \n ⊙\n \n -prime ideals and their relation.","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fuzzy Ideals in Pseudo-Hoop Algebras\",\"authors\":\"Teferi Getachew Alemayehu\",\"doi\":\"10.1155/2022/4643252\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, fuzzy ideals in pseudo-hoop algebras are presented. Also, we investigate fuzzy congruences relations on pseudo-hoop algebras induced by fuzzy ideals. By using fuzzy ideals, we create the fuzzy quotient pseudo-hoop algebras and identify and demonstrate the one-to-one relationship between the set of all normal fuzzy ideals of a pseudo-hoop algebra \\n \\n H\\n \\n with conditions \\n \\n \\n \\n p\\n \\n D\\n N\\n \\n \\n \\n and the set of all fuzzy congruences relation on \\n \\n H\\n \\n . Additionally, we investigate the relationship between fuzzy ideals and fuzzy filters in pseudo-hoop algebras by considering the set of complement elements of pseudo-hoop algebras. Lastly, we study fuzzy prime ideals and fuzzy \\n \\n ⊙\\n \\n -prime ideals and their relation.\",\"PeriodicalId\":301406,\"journal\":{\"name\":\"Int. J. Math. Math. Sci.\",\"volume\":\"38 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Math. Math. Sci.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2022/4643252\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Math. Math. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2022/4643252","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this study, fuzzy ideals in pseudo-hoop algebras are presented. Also, we investigate fuzzy congruences relations on pseudo-hoop algebras induced by fuzzy ideals. By using fuzzy ideals, we create the fuzzy quotient pseudo-hoop algebras and identify and demonstrate the one-to-one relationship between the set of all normal fuzzy ideals of a pseudo-hoop algebra
H
with conditions
p
D
N
and the set of all fuzzy congruences relation on
H
. Additionally, we investigate the relationship between fuzzy ideals and fuzzy filters in pseudo-hoop algebras by considering the set of complement elements of pseudo-hoop algebras. Lastly, we study fuzzy prime ideals and fuzzy
⊙
-prime ideals and their relation.
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