Let $A$ be a noetherian, graded ring and $M$ be a projective, graded $A$-module. Denote by $M_{\ge d}:=\oplus_{\ell \ge d} M_\ell$ the sub-module of $M$. Is $M_{\ge d}$ again a projective $A$-module?
Projective modules and gradings
Ron
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