{"title":"模块良好 I 滤波的希尔伯特系数","authors":"Le Xuan Dung","doi":"10.1142/s0219498825501932","DOIUrl":null,"url":null,"abstract":"Let $M$ be a finitely generated module of dimention d over a Noetherian local ring (A,m) and I an m-primary ideal. Let be a pair of good I-filtrations F and F' of M. We show that the Hilbert coefficients e_i(F) are bounded below and above in terms of i, e_0(F'),...,e_i(F'), and reduction numbers of F and F', for all i \\ge 1.","PeriodicalId":508127,"journal":{"name":"Journal of Algebra and Its Applications","volume":"16 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hilbert coefficients of good I-Filtrations of modules\",\"authors\":\"Le Xuan Dung\",\"doi\":\"10.1142/s0219498825501932\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $M$ be a finitely generated module of dimention d over a Noetherian local ring (A,m) and I an m-primary ideal. Let be a pair of good I-filtrations F and F' of M. We show that the Hilbert coefficients e_i(F) are bounded below and above in terms of i, e_0(F'),...,e_i(F'), and reduction numbers of F and F', for all i \\\\ge 1.\",\"PeriodicalId\":508127,\"journal\":{\"name\":\"Journal of Algebra and Its Applications\",\"volume\":\"16 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra and Its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219498825501932\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra and Its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219498825501932","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设 $M$ 是诺特局部环 (A,m) 上维数为 d 的有限生成模块，且 I 是 m 主 ideal。我们证明，对于所有 i \ge 1，希尔伯特系数 e_i(F)、e_0(F'),...,e_i(F')以及 F 和 F' 的还原数在下面和上面都是有界的。
Hilbert coefficients of good I-Filtrations of modules
Let $M$ be a finitely generated module of dimention d over a Noetherian local ring (A,m) and I an m-primary ideal. Let be a pair of good I-filtrations F and F' of M. We show that the Hilbert coefficients e_i(F) are bounded below and above in terms of i, e_0(F'),...,e_i(F'), and reduction numbers of F and F', for all i \ge 1.
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