Geodesic
On Global Dimensions of Tree Type Finite Dimensional Algebras
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 814-820

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DOI

A formula is provided to explicitly describe global dimensions of all kinds of tree type finite dimensional $k$ -algebras for $k$ an algebraic closed field. In particular, it is pointed out that if the underlying tree type quiver has $n$ vertices, then the maximum global dimension is $n\,-\,1$ .
DOI : 10.4153/CMB-2014-035-9
Mots-clés : 16D40, 16E10, 16G20, global dimension, tree type finite dimensional k-algebra, quiver 
Hou, Ruchen. On Global Dimensions of Tree Type Finite Dimensional Algebras. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 814-820. doi: 10.4153/CMB-2014-035-9
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     author = {Hou, Ruchen},
     title = {On {Global} {Dimensions} of {Tree} {Type} {Finite} {Dimensional} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {814--820},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2014-035-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-035-9/}
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