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Standard exact projective resolutions relative to a countable class of Fréchet spaces

100%

Domański P., Krone J., Vogt D.

Studia Mathematica

1997

tom 123

nr 3

275-290

We will show that for each sequence of quasinormable Fréchet spaces $(E_n)_ℕ$ there is a Köthe space λ such that $Ext^1(λ(A), λ(A) = Ext^1 (λ(A), E_n)=0$ and there are exact sequences of the form $... → λ(A) → λ(A) → λ(A) → λ(A) → {E_n} → 0$. If, for a fixed ℕ, $E_n$ is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form $0 → λ(A) → λ(A) → {E_n} → 0$. The result has some applications in the theory of the functor $Ext^1$ in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.

Decompositions of the category of noncommutative sets and Hochschild and cyclic homology

100%

Słomińska J.

Open Mathematics

2003

tom 1

nr 3

327-331

In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.

Ograniczanie wyników

1 Open Mathematics

1 Studia Mathematica

1 Domański P.

1 Krone J.

1 Słomińska J.

1 Vogt D.

1 2003

1 1997

Wyniki wyszukiwania

Standard exact projective resolutions relative to a countable class of Fréchet spaces

Decompositions of the category of noncommutative sets and Hochschild and cyclic homology