Section 6.3
Invertibility in monoids
In a monoid M with unit element e an element h is called the inverse of g if
g * h = h * g = e.
An element is called invertible if it has an inverse.
We will explain later that the use of the adjective `the' is justified.
If an element is invertible, then we can `divide':
Let x, y, z be elements of a monoid.
If x is invertible and x * y = x * z,
then
y = z.