Abstract
In this paper we devote to generalizing some results of componentwise linear modules over a polynomial ring to the ones over a Koszul algebra. Among other things, we show that the $i$-linear strand of the minimal free resolution of a componentwise linear module is the minimal free resolution of some module which is described explicitly for any $i\in Z$. In addition we present some theorems about when graded modules with linear quotients are componentwise linear.
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