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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 4, Pages 137–154 (Mi izv194)  

This article is cited in 4 scientific papers (total in 4 papers)

The problem of the existence of sufficiently many injective Frechet modules over non-normed Frechet algebras

A. Yu. Pirkovskii

M. V. Lomonosov Moscow State University

Abstract: The main aim of this paper is to show that in the category of Frechet modules over certain Frechet algebras there cannot exist sufficiently many injective objects. In particular, we show that over Frechet algebras of formal power series there are no non-zero injective Frechet modules. We describe a class of Frechet algebras, which includes algebras of holomorphic functions over irreducible Stein spaces, over which there is no injective metrizable hypermodule. We also study the property of divisibility for Frechet modules and its relationship with the property of injectivity. We also show that every separable divisible Frechet module has periodic elements and prove a theorem on the non-existence of divisible Banach modules.

DOI: https://doi.org/10.4213/im194

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English version:
Izvestiya: Mathematics, 1998, 62:4, 773–788

Bibliographic databases:

MSC: 46H25, 43A65, 18G05
Received: 27.03.1997

Citation: A. Yu. Pirkovskii, “The problem of the existence of sufficiently many injective Frechet modules over non-normed Frechet algebras”, Izv. RAN. Ser. Mat., 62:4 (1998), 137–154; Izv. Math., 62:4 (1998), 773–788

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pirkovskii A.Y., “On the nonexistence of cofree Frechet modules over locally multiplicatively-convex Frechet algebras”, Rocky Mountain Journal of Mathematics, 29:3 (1999), 1129–1138  crossref  mathscinet  zmath  isi  scopus
    2. A. Yu. Pirkovskii, “Weak homological dimensions and biflat Köthe algebras”, Sb. Math., 199:5 (2008), 673–705  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Pirkovskii, AY, “FLAT CYCLIC FRECHET MODULES, AMENABLE FRECHET ALGEBRAS, AND APPROXIMATE IDENTITIES”, Homology Homotopy and Applications, 11:1 (2009), 81  crossref  mathscinet  zmath  isi  scopus
    4. A. Yu. Pirkovskii, “Homological dimensions and Van den Bergh isomorphisms for nuclear Fréchet algebras”, Izv. Math., 76:4 (2012), 702–759  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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