{"title":"交换环上对准的初理想","authors":"Khurul Wardati","doi":"10.14421/fourier.2018.72.79-86","DOIUrl":null,"url":null,"abstract":"Definisi ideal dasar dan ideal bebas dalam aljabar bebas atas ring komutatif dengan elemen satuan adalah ekuivalen. Namun, ideal dasar dalam suatu aljabar tak bebas belum tentu merupakan ideal bebas, sementara ideal bebas pasti ideal dasar. Artikel ini membahas beberapa sifat ideal dasar prima dalam aljabar tak bebas atas ring komutatif dengan elemen satuan. \n[The definitions of basic ideal and free ideal in free algebras over a unital commutative ring are equivalen. However, a basic ideal in the non-free algebra is not neceearily a free ideal, while any free ideal is definitely a basic ideal. This paper will discuss some properties of prime basic ideal in non-free algebras over a unital commutative ring.]","PeriodicalId":55815,"journal":{"name":"Jurnal Fourier","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Ideal Dasar Prima Dalam Aljabar Atas Suatu Ring Komutatif\",\"authors\":\"Khurul Wardati\",\"doi\":\"10.14421/fourier.2018.72.79-86\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Definisi ideal dasar dan ideal bebas dalam aljabar bebas atas ring komutatif dengan elemen satuan adalah ekuivalen. Namun, ideal dasar dalam suatu aljabar tak bebas belum tentu merupakan ideal bebas, sementara ideal bebas pasti ideal dasar. Artikel ini membahas beberapa sifat ideal dasar prima dalam aljabar tak bebas atas ring komutatif dengan elemen satuan. \\n[The definitions of basic ideal and free ideal in free algebras over a unital commutative ring are equivalen. However, a basic ideal in the non-free algebra is not neceearily a free ideal, while any free ideal is definitely a basic ideal. This paper will discuss some properties of prime basic ideal in non-free algebras over a unital commutative ring.]\",\"PeriodicalId\":55815,\"journal\":{\"name\":\"Jurnal Fourier\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Jurnal Fourier\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.14421/fourier.2018.72.79-86\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Jurnal Fourier","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14421/fourier.2018.72.79-86","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ideal Dasar Prima Dalam Aljabar Atas Suatu Ring Komutatif
Definisi ideal dasar dan ideal bebas dalam aljabar bebas atas ring komutatif dengan elemen satuan adalah ekuivalen. Namun, ideal dasar dalam suatu aljabar tak bebas belum tentu merupakan ideal bebas, sementara ideal bebas pasti ideal dasar. Artikel ini membahas beberapa sifat ideal dasar prima dalam aljabar tak bebas atas ring komutatif dengan elemen satuan.
[The definitions of basic ideal and free ideal in free algebras over a unital commutative ring are equivalen. However, a basic ideal in the non-free algebra is not neceearily a free ideal, while any free ideal is definitely a basic ideal. This paper will discuss some properties of prime basic ideal in non-free algebras over a unital commutative ring.]
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