{"title":"同质理想与雅各布森基","authors":"N.G. Najaryan","doi":"10.46991/pysu:a/2017.51.2.193","DOIUrl":null,"url":null,"abstract":"In this paper the Jacobson radical of an algebra$F\\langle X\\rangle / H$ is studied, where FhXi is a free associative algebra of countable rank over infinite field $F$ and $H$ is a homogeneous ideal of the algebr$F\\langle X\\rangle$. The following theorem is proved: the Jacobson radical of an algebra $F\\langle X\\rangle / H$ is a nil ideal.","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"111 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"HOMOGENEOUS IDEALS AND JACOBSON RADICAL\",\"authors\":\"N.G. Najaryan\",\"doi\":\"10.46991/pysu:a/2017.51.2.193\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper the Jacobson radical of an algebra$F\\\\langle X\\\\rangle / H$ is studied, where FhXi is a free associative algebra of countable rank over infinite field $F$ and $H$ is a homogeneous ideal of the algebr$F\\\\langle X\\\\rangle$. The following theorem is proved: the Jacobson radical of an algebra $F\\\\langle X\\\\rangle / H$ is a nil ideal.\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"111 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2017.51.2.193\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2017.51.2.193","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper the Jacobson radical of an algebra$F\langle X\rangle / H$ is studied, where FhXi is a free associative algebra of countable rank over infinite field $F$ and $H$ is a homogeneous ideal of the algebr$F\langle X\rangle$. The following theorem is proved: the Jacobson radical of an algebra $F\langle X\rangle / H$ is a nil ideal.
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