On functors with given derivatives
type: Item
instance of: scholarly article
title: On functors with given derivatives
zbMATH Open document ID: 0787.18009
DOI: 10.1007/BF02988475
author: M. B. Zvyagina
published in: Journal of Soviet Mathematics
publication date: 1993-09-01T00:00:00Z
review text: For a functor \(F: {_ \Lambda\text{Mod}}\to{_ \mathbb{Z}\text{Mod}}\) from the category of \(\Lambda\)-modules to the category of Abelian groups let \(L_ i F\) (resp. \(R_ i F\)) denote the \(i\)th left (resp., right) derived functor of \(F\). The author examines the following (A. V. Jakovlev's) property of \(\Lambda\): For given \(\Lambda\)-modules \(A\) and \(B\) there is a covariant functor \(_ B F_ A: { _ \Lambda\text{Mod}}\to {_ \mathbb{Z}\text{Mod}}\) such that \(L_{iB} F_ A=\text{Tor}_ \Lambda^ i(A,-)\) and \(R_{iB} F_ A=\text{Ext}^ i_ \Lambda(B,-)\) for \(i=1,2,\dots\;\). Then some sufficient (but not necessary) nice conditions for rings \(\Lambda\) satisfying that property are presented.
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 18E25
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 18G15
zbMATH DE Number: 404561
zbMATH Keywords: derived functors
zbMATH Keywords: right semisimple ring of fractions
reviewed by: Marek Golasiński
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02988475
OpenAlex ID: W2080653301
description: scientific article; zbMATH DE number 404561