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.