In this article,we study the McCoy modules of cyclic modules and finitely generated modules over a McCoy ring.We show that a left cyclic module over a McCoy ring is a McCoy module under some condition.We give examples to show that a simple module over a McCoy ring is McCoy and a simple module over a non-McCoy ring is McCoy respectively.We also show that the finitely generated free modules under some conditions over a ring R are McCoy if and only if the ring R is McCoy.
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