Biprojective topological algebras of homological bidimension 1
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.
scientific article; zbMATH DE number 1821734