Filtrations and homological degrees of FI-modules

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• 作者：Liping Li^a ; ^{lipingli@hunnu.edu.cn} ; Nina Yu^b ; ^{ninayu@xmu.edu.cn}
• 关键词：FI-modules ; Filtrations ; Homological degrees ; Projective dimensions
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：472
• 期：Complete
• 页码：369-398
• 全文大小：471 K
• 卷排序：472

文摘

Let kk be a commutative Noetherian ring. In this paper we consider ♯-filtered modules of the category FIFI firstly introduced in [12]. We show that a finitely generated FIFI-module V   is ♯-filtered if and only if its higher homologies all vanish, and if and only if a certain homology vanishes. Using this homological characterization, we characterize finitely generated CC-modules V   whose projective dimension pd(V)pd(V) is finite, and describe an upper bound for pd(V)pd(V). Furthermore, we give a new proof for the fact that V induces a finite complex of ♯-filtered modules, and use it as well as a result of Church and Ellenberg in [1] to obtain another upper bound for homological degrees of V.