I was reviewing my class notes and found the following:
"The name 'torsion' comes from topology and refers to spaces that are twisted, ex. Möbius band"
In our notes we used the following definition for torsion element and torsion module: An element m of an R-module M is called a torsion element if $rm=0$ for some $r\in R$. A torsion module is a module which consists solely of torsion elements
What is the relationship between torsion modules and twisted spaces? Was the definition of torsion module somehow motivated from topological considerations of twisted spaces?
I don't really see any obvious connection. I'm taking my first topology class this semester, so I apologize if this is something you learn about later in courses like algebraic topology, but I haven't been able to find any explanation of this.