# Module projective

Is this relation true?

• $M$ is projective module if and only if $M_m$ is projective module for every maximal ideal $m$.
• $M$ is finitely generated free module if and only if $M_m$ is finitely generated free module for every maximal $w$-ideal $m$.

Thank you so much

• What is $M$? What is $M_m$? What is $w$? – Kevin Long Nov 15 '17 at 19:05
• I'am so sorry. $M$ and $M_m$ are module and $w$ is operation as star operation. – mohammed Nov 15 '17 at 23:56