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Regular, inverse, and completely regular centralizers of permutations

Janusz Konieczny (2003)

Mathematica Bohemica

For an arbitrary permutation σ in the semigroup T n of full transformations on a set with n elements, the regular elements of the centralizer C ( σ ) of σ in T n are characterized and criteria are given for C ( σ ) to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.

Riemann surfaces in Stein manifolds with the Density property

Rafael B. Andrist, Erlend Fornæss Wold (2014)

Annales de l’institut Fourier

We show that any open Riemann surface can be properly immersed in any Stein manifold with the (Volume) Density property and of dimension at least 2. If the dimension is at least 3, we can actually choose this immersion to be an embedding. As an application, we show that Stein manifolds with the (Volume) Density property and of dimension at least 3, are characterized among all other complex manifolds by their semigroup of holomorphic endomorphisms.

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