I want to know the answer to the following question:
What method formally adds inverses to elements to any monoid?
All the background I'm provided with is that "There is a general method to formally add inverses to elements to any (abelian) monoid, much the same way as (Q ∖ {0}, ·) is derived from (Z ∖ {0}, ·), known as the Grothendieck group.". Is that enough to answer the question?