I'm learning about periodic languages, and I'm confused over the vocabulary used to describe the periodicity of (syntactic) monoids.

If I understand correctly, a monoid M is *periodic* if :
$$(\forall m \in M)(\exists i \neq j)[m^i = m^j],$$
and it is *aperiodic* if :
$$(\exists k)(\forall m \in M)[m^k = m^{k+1}],$$
and then an aperiodic monoid is periodic. Where does that bizarre vocabulary come from?

And in the same vein, what would be the book you'd recommend on monoids and semigroups?

Thank you.