Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-10,
author = {Ibrahim Assem and Dan Zacharia},
title = {On split-by-nilpotent extensions},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {259-275},
zbl = {1065.16007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-10}
}
Ibrahim Assem; Dan Zacharia. On split-by-nilpotent extensions. Colloquium Mathematicae, Tome 96 (2003) pp. 259-275. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-10/