The vanishing of self-extensions over $n$-symmetric algebras of quasitilted type
Volume 136 / 2014
Colloquium Mathematicum 136 (2014), 99-108
MSC: Primary 16D50, 16G99, 16E65.
DOI: 10.4064/cm136-1-9
Abstract
A ring $\varLambda $ satisfies the Generalized Auslander–Reiten Condition $(\mathsf {GARC})$ if for each $\varLambda $-module $M$ with $\operatorname {Ext}^i(M,M\oplus \varLambda )=0$ for all $i>n$ the projective dimension of $M$ is at most $n$. We prove that this condition is satisfied by all $n$-symmetric algebras of quasitilted type.
