Spring 2024 ON THE PARTIAL EULER–POINCARÉ CHARACTERISTICS OF KOSZUL COMPLEXES OF IDEALIZATION
Pham Hong Nam
J. Commut. Algebra 16(1): 75-93 (Spring 2024). DOI: 10.1216/jca.2024.16.75

Abstract

Let (R,𝔪) be a Noetherian local ring and M be a finitely generated R-module. In this paper, we give precise formulas computing all the partial Euler–Poincaré characteristics of Koszul complexes of the idealization RM with respect to an almost p-standard system of parameters (a strict subclass of d-sequences) in terms of multiplicities of certain subquotients of R and M. As an application, we clarify the invariants pk(RM) of the idealization RM that were introduced by N. T. Cuong and Khoi (1996).

Citation

Download Citation

Pham Hong Nam. "ON THE PARTIAL EULER–POINCARÉ CHARACTERISTICS OF KOSZUL COMPLEXES OF IDEALIZATION." J. Commut. Algebra 16 (1) 75 - 93, Spring 2024. https://doi.org/10.1216/jca.2024.16.75

Information

Received: 7 December 2022; Accepted: 6 September 2023; Published: Spring 2024
First available in Project Euclid: 18 January 2024

MathSciNet: MR4690596
zbMATH: 07823248
Digital Object Identifier: 10.1216/jca.2024.16.75

Subjects:
Primary: 13D03 , 13H10 , 13H15

Keywords: almost p-standard system of parameters , d-sequence , Idealization , multiplicity , partial Euler–Poincaré characteristics

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
19 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.16 • No. 1 • Spring 2024
Back to Top