Biprojective topological algebras of homological bidimension 1
type: Item
instance of: scholarly article
title: Biprojective topological algebras of homological bidimension 1
zbMATH Open document ID: 1025.46018
DOI: 10.1023/A:1016058211668
published in: Journal of Mathematical Sciences (New York)
publication date: 2003-12-02T00:00:00Z
review text: A locally convex topological algebra \(A\) is called biprojective if it is projective as a bimodule over itself, and the homological bidimension db \(A\) of \(A\) is the homological dimension of \(A_+\) considered as an \(A\)-bimodule where \(A_+\) denotes the unitization of \(A\) [see \textit{A. Ya. Khelemskij}, ``The homology of Banach and topological algebras'', Kluwer, Dordrecht (1989; Zbl 0695.46033)]. Conditions for biprojective Köthe algebras to have bidimension 1 are studied. Nuclearity is necessary, and additional properties to imply the converse are given. In order to construct new examples of biprojective algebras, it is shown that db \(A\leq 1\) implies db \(B\leq 1\) for biprojective algebras if there exists a homomorphism \(\varphi: A\to B\) satisfying certain nondegeneracy and flatness conditions.
reviewed by: Gerhard Garske
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 46M20
zbMATH DE Number: 1821734
zbMATH Keywords: biprojective algebras
author: A. Yu. Pirkovskii
MaRDI profile type: Publication
full work available at URL: a:1016058211668
OpenAlex ID: W174420338
description: scientific article; zbMATH DE number 1821734