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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-10,
author = {Adam Hajduk},
title = {CB-degenerations and rigid degenerations of algebras},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {305-310},
zbl = {1122.16013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-10}
}
Adam Hajduk. CB-degenerations and rigid degenerations of algebras. Colloquium Mathematicae, Tome 106 (2006) pp. 305-310. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-10/