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

Studia Mathematica (1999)

- Volume: 133, Issue: 2, page 163-174
- ISSN: 0039-3223

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topPirkovskii, A.. "On Arens-Michael algebras which do not have non-zero injective ⨶-modules." Studia Mathematica 133.2 (1999): 163-174. <http://eudml.org/doc/216611>.

@article{Pirkovskii1999,

abstract = {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.},

author = {Pirkovskii, A.},

journal = {Studia Mathematica},

keywords = {Arens-Michael algebras; non-zero injective topological -modules; algebras of holomorphic functions on polydomains; algebras of smooth functions on domains; formal power series; nuclear Fréchet-Arens-Michael algebra; bimodule Koszul resolution},

language = {eng},

number = {2},

pages = {163-174},

title = {On Arens-Michael algebras which do not have non-zero injective ⨶-modules},

url = {http://eudml.org/doc/216611},

volume = {133},

year = {1999},

}

TY - JOUR

AU - Pirkovskii, A.

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

JO - Studia Mathematica

PY - 1999

VL - 133

IS - 2

SP - 163

EP - 174

AB - 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.

LA - eng

KW - Arens-Michael algebras; non-zero injective topological -modules; algebras of holomorphic functions on polydomains; algebras of smooth functions on domains; formal power series; nuclear Fréchet-Arens-Michael algebra; bimodule Koszul resolution

UR - http://eudml.org/doc/216611

ER -

## References

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- [9] A. Yu. Pirkovskii, shape On the non-existence of cofree Fréchet modules over non-normable locally multiplicatively convex Fréchet algebras, Rocky Mountain J. Math., to appear.
- [10] A. Yu. Pirkovskii, shape On the existence problem for a sufficient family of injective Fréchet modules over non-normable Fréchet algebras, Izv. Ross. Akad. Nauk Ser. Mat. 62 (1998), no. 4, 137-154 (in Russian).
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