{"title":"移位模、强稳定理想及其对偶性","authors":"Gunnar Fløystad","doi":"10.1090/btran/137","DOIUrl":null,"url":null,"abstract":"We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSIs. The recently introduced duality on SSIs is given an effective conceptual and computational setting. We study SSIs in infinite dimensional polynomial rings, where the duality is most natural. Finally a new type of resolution for SSIs is introduced. This is the projective resolution in the category of shift modules.","PeriodicalId":377306,"journal":{"name":"Transactions of the American Mathematical Society, Series B","volume":"28 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Shift modules, strongly stable ideals, and their dualities\",\"authors\":\"Gunnar Fløystad\",\"doi\":\"10.1090/btran/137\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSIs. The recently introduced duality on SSIs is given an effective conceptual and computational setting. We study SSIs in infinite dimensional polynomial rings, where the duality is most natural. Finally a new type of resolution for SSIs is introduced. This is the projective resolution in the category of shift modules.\",\"PeriodicalId\":377306,\"journal\":{\"name\":\"Transactions of the American Mathematical Society, Series B\",\"volume\":\"28 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the American Mathematical Society, Series B\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/btran/137\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/btran/137","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Shift modules, strongly stable ideals, and their dualities
We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSIs. The recently introduced duality on SSIs is given an effective conceptual and computational setting. We study SSIs in infinite dimensional polynomial rings, where the duality is most natural. Finally a new type of resolution for SSIs is introduced. This is the projective resolution in the category of shift modules.
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