Graded algebras and their Euler-Poincaré series
type: Item
instance of: scholarly article
title: Graded algebras and their Euler-Poincaré series
zbMATH Open document ID: 0619.13006
DOI: 10.1016/0022-4049(87)90091-0
published in: Journal of Pure and Applied Algebra
publication date: 1987-01-01T00:00:00Z
review text: Let k be a field, R a connected graded k-algebra and M a graded R-module, both R and M finitely generated as k-modules in each degree. Let [M] be the Hilbert series of M, i.e., \([M]=\sum (\dim_ kM_ i)t^ i\quad and\) let \([H_*(R,M)]\) be \(\sum (-1)^ i\dim_ k(Tor_ i^ R(k,M))t^ i.\quad Then\) it is well known that \([M]=[R]\cdot [H_*(R,M)]\). This result is generalized in this article to the case where k is a commutative Noetherian regular ring. Also a result by Lemaire on the relation between the Hilbert series of the components of a fibre product is generalized in the same way. This also has a dual form concerning free products with amalgamation.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13H05
zbMATH DE Number: 4004327
zbMATH Keywords: Euler-Poincaré series
zbMATH Keywords: graded algebras
zbMATH Keywords: Hilbert series
zbMATH Keywords: regular ring
zbMATH Keywords: amalgamation
author: L. Grunenfelder
MaRDI profile type: Publication
full work available at URL: 0022-4049(87)90091-0
OpenAlex ID: W2048496652
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description: scientific article; zbMATH DE number 4004327