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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 32, Pages 1679-1701
http://dx.doi.org/10.1155/S0161171204309270

On the Beurling algebras Aα+(𝔻)—derivations and extensions

Fachbereich Mathematik-Informatik, Gesamthochschule Paderborn, Paderborn 33095, Germany

Received 27 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Based on a description of the squares of cofinite primary ideals of Aα+(𝔻), we prove the following results: for α1, there exists a derivation from Aα+(𝔻) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m and α[m,m+1), every finite-dimensional extension of Aα+(𝔻) splits algebraically if and only if αm+1/2.