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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 global dimension, tree type finite dimensional $k-$algebra, quiver
MSC Classifications: 16D40, 16E10, 16G20 show english descriptions Free, projective, and flat modules and ideals [See also 19A13]
Homological dimension
Representations of quivers and partially ordered sets
16D40 - Free, projective, and flat modules and ideals [See also 19A13]
16E10 - Homological dimension
16G20 - Representations of quivers and partially ordered sets
 

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