Abstract

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We introduce a new numerical invariant called cone length for DG modules 

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over a DG algebra. This invariant plays a similar role as projective 

<br>
dimension of a module over a ring does in homological ring theory.  We 

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discover some of its upper and lower bounds and find that it has a close

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relations with other invariants such as ghost length and level of a DG 

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module.  The left (resp. right) global dimension of a DG algebra A is 

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defined as the supremum of the set of cone lengths of all left (resp. 

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right) DG A-modules.  It is proved that our definition is a generalization 

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of that of graded algebras.  Some relations between the global dimension 

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of H(A) and the left (resp. right) global dimension of A are discovered. 

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If A is homologically smooth, then we prove that the left (right) global 

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dimension of A is finite and the dimension of D^c (A) is not bigger than 

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the DG free class of a minimal semi-free resolution X of the DG A^e-module A.