What is the meaning of saying following: Let $P$ be a finitely presented $A[X]$ module. Suppose $P$ is extended from $A$?

Question

What is the meaning of saying following:

Let $P$ be a finitely presented $A[X]$ module. Suppose $P$ is extended from $A$?

I've not seen the above terminology.Could anyone please explain?

Answer 1

This means $P$ is obtained from some $A$-module by extension of scalars, i.e. there exists an $A$-module $M$ such that $$P\simeq M\otimes_A A[X]\enspace\text{as $A[X]$-modules.}$$