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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## On split-by-nilpotent extensions

### Tom 98 / 2003

Colloquium Mathematicum 98 (2003), 259-275 MSC: 16G20, 16G70. DOI: 10.4064/cm98-2-10

#### Streszczenie

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.

#### Autorzy

• Ibrahim AssemDépartement de Matématiques
Université de Sherbrooke
Sherbrooke, Québec