The main aim of this note is to prove that if k is an algebraically closed field and a k-algebra A₀ is a CB-degeneration of a finite-dimensional k-algebra A₁, then there exists a factor algebra Ā₀ of A₀ of the same dimension as A₁ such that Ā₀ is a CB-degeneration of A₁. As a consequence, Ā₀ is a rigid degeneration of A₁, provided A₀ is basic.

For a split graph order ℒ over a complete local regular domain $𝒪$ of dimension 2 the indecomposable Cohen-Macaulay modules decompose - up to irreducible projectives - into a union of the indecomposable Cohen-Macaulay modules over graph orders of type •—• . There, the Cohen-Macaulay modules filtered by irreducible Cohen-Macaulay modules are in bijection to the homomorphisms $\varphi :𝒪L^{\left(\mu \right)}\to 𝒪L^{\left(\nu \right)}$ under the bi-action of the groups $\left(Gl\right(\mu ,𝒪L),Gl(\nu ,𝒪L\left)\right)$, where $𝒪L=𝒪/〈\pi 〉$ for a prime π. This problem strongly depends on the nature of $𝒪L$. If $𝒪L$ is regular,...