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On Global Dimensions of Tree Type Finite Dimensional Algebras

Published:2014-09-13
Printed: Dec 2014
• Ruchen Hou,
Department of Mathematics and Information Science, Yantai University, Yantai, 264005, P. R. China
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Abstract

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 of possible global dimensions is $n-1$.
 Keywords: global dimension, tree type finite dimensional $k-$algebra, quiver
 MSC Classifications: 16D40 - Free, projective, and flat modules and ideals [See also 19A13] 16E10 - Homological dimension 16G20 - Representations of quivers and partially ordered sets