Geodesic
The vanishing of self-extensions over $n$-symmetric algebras of quasitilted type
Maciej Karpicz1 ; Marju Purin2
1Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2Department of Mathematics, Statistics and Computer Science St. Olaf College Northfield, MN 55057, U.S.A.
Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 99-108
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm136-1-9
Keywords: ring varlambda satisfies generalized auslander reiten condition mathsf garc each varlambda module operatorname ext oplus varlambda projective dimension prove condition satisfied n symmetric algebras quasitilted type

Maciej Karpicz  1   ; Marju Purin  2

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2 Department of Mathematics, Statistics and Computer Science St. Olaf College Northfield, MN 55057, U.S.A. 
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Maciej Karpicz; Marju Purin. The vanishing of self-extensions
 over $n$-symmetric algebras of quasitilted type. Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 99-108. doi: 10.4064/cm136-1-9

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