CB-degenerations and rigid degenerations of algebras
Volume 106 / 2006
Colloquium Mathematicum 106 (2006), 305-310
MSC: 16G60, 14A10.
DOI: 10.4064/cm106-2-10
Abstract
The main aim of this note is to prove that if $k$ is an algebraically closed field and a $k$-algebra $A_0$ is a CB-degeneration of a finite-dimensional $k$-algebra $A_1$, then there exists a factor algebra $\,\overline{\!A}_0$ of $A_0$ of the same dimension as $A_1$ such that $\,\overline{\!A}_0$ is a CB-degeneration of $A_1$. As a consequence, $\,\overline{\!A}_0$ is a rigid degeneration of $A_1$, provided $A_0$ is basic.
