Document Type: Original Manuscript


Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran.


Let $R$ be a commutative Noetherian ring, $fa$ an
ideal of $R$ and $mathcal{D}(R)$ denote the derived category of
$R$-modules. For any homologically bounded complex $X$, we conjecture that
$sup {bf L}Lambda^{fa}(X)leq$ mag$_RX$. We prove this
in several cases. This generalize the main result of Hatamkhani and Divaani-Aazar cite{HD} for complexes.