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 α≥1, there exists a derivation from Aα+(𝔻) into a finite-dimensional module such that this derivation is unbounded on every dense subalgebra; for m∈ℕ and α∈[m,m+1), every finite-dimensional extension of Aα+(𝔻) splits algebraically if and only if α≥m+1/2.