Mittag-Leffler condition and the vanishing of \(\varprojlim^ 1\)
type: Item
instance of: scholarly article
title: Mittag-Leffler condition and the vanishing of \(\varprojlim^ 1\)
zbMATH Open document ID: 0864.18005
DOI: 10.1016/0040-9383(94)00056-5
author: Ioannis Emmanouil
published in: Topology
publication date: 1996-04-08T00:00:00Z
review text: The author considers inverse limits \(\varprojlim\) of (right) modules over a fixed ring \(k\), with indexing category the natural numbers \(\mathbb{N}\). An inverse system \(\Xi= (X_m)_{m\in\mathbb{N}}\) satisfies the Mittag-Leffler condition if for all \(n\) the decreasing filtration of \(X_n\) formed by the images of \(X_m\) for \(m>n\) is eventually constant. The main results are the following: an inverse system \(\Xi\) satisfies the Mittag-Leffler condition if and only if \(\varprojlim^1 (\Xi\otimes E)=0\) for any left \(k\)-module \(E\) if and only if \(\varprojlim^1 (\Xi \otimes K)=0\) for any ring extension \(K\) of \(k\).
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 16E30
zbMATH DE Number: 863703
zbMATH Keywords: inverse limits
zbMATH Keywords: Mittag-Leffler condition
reviewed by: Leslie G. Roberts
MaRDI profile type: Publication
full work available at URL: 0040-9383(94)00056-5
OpenAlex ID: W2081589340
description: scientific article; zbMATH DE number 863703