abelian group

1986, Partially Ordered Abelian Groups with Interpolation, American Mathematical Society, 2010 softcover reprint, page 12, Let G and H be partially ordered abelian groups. A positive homomorphism from G to H is any abelian group homomorphism f:G→H that maps positive elements to positive elements, that is, f(G⁺)⊆H⁺.

2000, David Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets, Springer, Softcover reprint of 1st edition, page 74, Chapter 2 is a brief introduction to some fundamental techniques for countable torsion-free abelian groups.