CB-degenerations and rigid degenerations of algebras

Volume 106 / 2006

Adam Hajduk 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.

Authors

  • Adam HajdukFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

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