Addition theorems in partially ordered groups
Melvyn B. Nathanson · arXiv (Cornell University) · 2024
Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results are inherently order-theoretic and extend to partially ordered abelian and nonabelian groups. One abelian application is an addition theorem for sums of sets of $n$-dimensional lattice points.