A Study of the Length Function of Generalized Fractions of Modules. Issue 3 (2nd November 2016)

• Record Type: Journal Article
• Authors: Morales, Marcel; Quy, Pham Hung
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 60:Issue 3(2017)
• Page Start: 721
• Page End: 737
• Publication Date: 2016-11-02
• Subjects: system of parameters, -- generalized fractions, -- limit closure, -- local cohomology, -- Hilbert–Kunz function; Primary 13H15, -- 13D40, -- 13D45; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091516000237
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: Let be a Noetherian local ring and let M be a finitely generated R -module of dimension d . Let be a system of parameters of M and let be a d -tuple of positive integers. In this paper we study the length of generalized fractions M (1/( x 1, …, xd, 1)), which was introduced by Sharp and Hamieh. First, we study the growth of the function Then we give an explicit calculation for the function in the case in which M admits a certain Macaulay extension. Most previous results on this topic are improved in a clearly understandable way.