In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and is a good V-module.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-2-10,
author = {Eduardo do N. Marcos and Hector A. Merklen and Corina S\'aenz},
title = {Standardly stratified split and lower triangular algebras},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {303-311},
zbl = {1058.16016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-2-10}
}
Eduardo do N. Marcos; Hector A. Merklen; Corina Sáenz. Standardly stratified split and lower triangular algebras. Colloquium Mathematicae, Tome 91 (2002) pp. 303-311. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-2-10/