I have some background in commutative ring theory. At the moment I am going through factorization theory of integral domains.
I found out that it is a conjecture, that every Abelian group is the class group of a half-factorial Dedekind domain. I also read, that this was shown for Warfield groups, which are (after Wikipedia) summands of simply presented Abelian groups.
I could not find the definition of a simply presented Abelian group. Has it to do with a presentation of a group by some generating system wrt. some relations? Or is it more like being a finitely presented $\mathbb{Z}$-module?
Can somebody give a definition?