On Arens-Michael algebras which do not have non-zero injective ⨶-modules

Volume 133 / 1999

A. Pirkovskii Studia Mathematica 133 (1999), 163-174 DOI: 10.4064/sm-133-2-163-174


A certain class of Arens-Michael algebras having no non-zero injective topological ⨶-modules is introduced. This class is rather wide and contains, in particular, algebras of holomorphic functions on polydomains in $ℂ^n$, algebras of smooth functions on domains in $ℝ^n$, algebras of formal power series, and, more generally, any nuclear Fréchet-Arens-Michael algebra which has a free bimodule Koszul resolution.


  • A. Pirkovskii

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