Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration such that for all t. Given a module M with square-free top and a projective cover P, she showed that if and only if M has no proper degeneration where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from our results. In particular, we find that her second result holds not just for modules with square-free top, but also for indecomposable modules in general.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-1-6,
author = {S. O. Smal\o\ and A. Valenta},
title = {Top-stable and layer-stable degenerations and hom-order},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {63-71},
zbl = {1113.16018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-1-6}
}
S. O. Smalø; A. Valenta. Top-stable and layer-stable degenerations and hom-order. Colloquium Mathematicae, Tome 107 (2007) pp. 63-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-1-6/