Definition of $p$-torsion module

Question

Let $p$ be a prime. What is the definition of a $p$-torsion module ? I have googled but was not convinced.

Answer 1

Let $\;M\;$ be a module over a ring $\;R\;$, then

$$M_p:=\left\{ x\in M\;;\;x^{p^n}=1\;,\;\;p\;\text{a fixed prime}\;,\;n\in\Bbb N\;\right\}$$

is called the $\;p-$ torsion submodule of $\;M\;$ .